arXiv subjects

Keiichi Watanabe

Publications and source records attributed to Keiichi Watanabe.

At least 19 recordsLinked to original sources

arXiv2025

Global well-posedness for the Keller--Segel--Navier--Stokes system with nonlinear boundary conditions

In this paper, we consider the Keller--Segel--Navier--Stokes system with nonlinear boundary conditions in a bounded smooth (and not necessarily convex) domain $\Omega \subset \mathbb{R}^N$, $N \ge 2$, where the chemotactic sensitivity $S$ is assumed to have values in $\mathbb{R}^{N \times N}$ which accounts for rotational fluxes. In contrast to the case where $S$ is a scalar-valued function (or $S$ is the identity matrix), in our system, the normal derivative for the density $n$ of the cell is given as the product of the unknown functions, i.e., the function $n$ satisfies the nonlinear boundary condition. We show the existence and uniqueness of global strong solutions to the system under the smallness assumptions of given data, where the Lipschitz continuity of the solution mapping and the asymptotic stability of the solution are also shown. The proof is based on maximal regularity results for the linear heat equation and the Stokes system, where we establish a new maximal regularity theorem for some linear heat equation with an inhomogeneous Neumann boundary condition. Since we develop a direct approach to construct the solutions (i.e., without considering limiting procedure in certain regularized problem with homogeneous linear boundary conditions), our solutions indeed satisfy the boundary conditions, which was not addressed clearly in the previous contributions by Cao and Lankeit (2016) as well as Yu, Wang, and Zheng (2018). Under suitable regularity conditions on given data, the solution may be understood in a classical sense and, as a by-product, the non-negativity result is proved via the maximum principle of a new type.

math.AP↗

arXiv2025

Revisiting Q-ball Interactions with Matters

Q-ball dark matter is one of the candidates for the macroscopic dark matter: Q-ball is a non-topological solitonic configuration, whose stability can be ensured by global charge and energy conservation. One of the crucial factors for discovering signatures from the Q-ball dark matter, is the interactions of the Q-ball dark matter with ordinary matter. In particular, the scattering of ordinary matter off the Q-ball dark matter is important for the direct detection searches, such as paleo-detectors. It was conjectured that quarks incident on the Q-ball were reflected as anti-quarks with a probability of order unity, but it costs the energy of the squark in the Q-ball, which cannot be paid in the scattering of ordinary matter off the Q-ball dark matter. In addition, once a proton is reflected as an anti-proton, the Q-ball obtains the electromagnetic charge. In this study, we revisit the scattering process of quarks with the Q-ball with taking into account the energy cost of the scattering and the electromagnetic charge-up of the Q-ball.

hep-ph↗

arXiv2025

Global Neutrino Constraints on the Minimal U(1)$_{L_\mu-L_\tau}$ Model

We examine the minimal U(1)$_{L_\mu-L_\tau}$ gauge model in light of the latest neutrino data, including neutrino oscillations, cosmological observations, direct mass measurements, and neutrinoless double-beta decay. Using the most conservative oscillation data, we find that normal ordering is excluded at approximately the 90% confidence level (CL). Incorporating cosmological constraints from Cosmic Microwave Background (CMB) observations strengthens this exclusion to about 95% CL, while further including Baryon Acoustic Oscillation (BAO) data increases it to nearly 99% CL. The inverted ordering is even more strongly disfavored. Our analysis is performed within a frequentist framework, minimizing sensitivity to prior assumptions inherent in Bayesian approaches. These results impose strong constraints on the viability of the minimal U(1)$_{L_\mu-L_\tau}$ gauge model.

hep-ph↗

arXiv2024

Comprehensive Bayesian Exploration of Froggatt-Nielsen Mechanism

The Froggatt-Nielsen (FN) mechanism successfully explains the hierarchical structure of fermion Yukawa couplings by introducing a U(1) flavor symmetry with distinct charge assignments for different fermion generations. While some FN charge assignments have been proposed, their evaluation has largely relied on heuristic approaches. This paper systematically investigates viable FN charge assignments within the Standard Model, including both the quark and lepton sectors, using Bayesian statistical analysis. The study explores scenarios involving both the seesaw mechanism and dimension-five operators for neutrino mass generation. A comprehensive parameter scan over FN charges reveals a wide range of charge assignments consistent with observed fermion masses and mixing angles. Interestingly, negative FN charges and significant generational differences in charges are found to be viable, contrary to conventional assumptions. The analysis also compares the seesaw mechanism and dimension-five operator scenarios, finding no strong preference between them for optimal charge assignments. Furthermore, predictions for the lightest neutrino mass and effective Majorana mass relevant for neutrinoless double-beta decay are presented, highlighting regions of parameter space accessible to upcoming experiments. Finally, implications for nucleon decay are studied, demonstrating that different FN charge assignments predict significantly different nucleon decay lifetimes and branching ratios, providing a potential experimental probe for FN models.

hep-ph↗

arXiv2024

Nucleon Decay as a Probe of Flavor Symmetry: The Case of Fake Unification

This paper explores nucleon decay within the framework of a "fake Grand Unified Theory (GUT)" combined with the Froggatt-Nielsen (FN) mechanism. In this fake GUT framework, quarks and leptons may have distinct high-energy origins but fit into complete $\mathrm{SU}(5)$ multiplets at low energies without requiring force unification, setting it apart from conventional GUTs. By introducing flavor symmetry through the FN mechanism, the model addresses the flavor puzzle of quark and lepton mass hierarchies and mixing patterns. Our analysis demonstrates that nucleon decay rates and branching fractions in the fake GUT are sensitive to flavor symmetry, providing a means to distinguish it from conventional GUT predictions. These findings underscore the importance of nucleon decay searches in probing both baryon number violation and the underlying flavor structure.

hep-ph↗

arXiv2024

Global strong solutions to the compressible Navier--Stokes--Coriolis system for large data

We consider the compressible Navier--Stokes system with the Coriolis force on the $3$D whole space. In this model, the Coriolis force causes the linearized solution to behave like a $4$th order dissipative semigroup $\{ e^{-t\Delta^2} \}_{t>0}$ with slower time decay rates than the heat kernel, which creates difficulties in nonlinear estimates in the low-frequency part and prevents us from constructing the global strong solutions by following the classical method. On account of this circumstance, the existence of unique global strong solutions has been open even in the classical Matsumura--Nishida framework. In this paper, we overcome the aforementioned difficulties and succeed in constructing a unique global strong solution in the framework of scaling critical Besov spaces. Furthermore, our result also shows that the global solution is constructed for arbitrarily large initial data provided that the speed of the rotation is high and the Mach number is low enough by focusing on the dispersive effect due to the mixture of the Coriolis force and acoustic wave.

math.AP↗

arXiv2024

Compressible Navier--Stokes--Coriolis system in critical Besov spaces

We consider the three-dimensional compressible Navier--Stokes system with the Coriolis force and prove the long-time existence of a unique strong solution. More precisely, we show that for any $0<T<\infty$ and arbitrary large initial data in the scaling critical Besov spaces, the solution uniquely exists on $[0,T]$ provided that the speed of rotation is high and the Mach numbers are low enough. To the best of our knowledge, this paper is the first contribution to the well-posedness of the \textit{compressible} Navier--Stokes system with the Coriolis force in the whole space $\mathbb R^3$. The key ingredient of our analysis is to establish the dispersive linear estimates despite a quite complicated structure of the linearized equation due to the anisotropy of the Coriolis force.

math.AP↗

arXiv2024

Small Instanton Effects on Composite Axion Mass

This paper investigates the impact of small instanton effects on the axion mass in composite axion models. In particular, we focus on the Composite Accidental Axion (CAA) models, which are designed to address the axion quality problem, and where the Peccei-Quinn (PQ) symmetry emerges accidentally. In the CAA models, the QCD gauge symmetry is embedded in a larger gauge group at high energy. These models contain small instantons not included in low-energy QCD, which could enhance the axion mass significantly. However, in the CAA models, our analysis reveals that these effects on the axion mass are non-vanishing but are negligible compared to the QCD effects. The suppression of the small instanton effects originates from the global chiral U(1) symmetries which are not broken spontaneously and play a crucial role in eliminating $θ$-terms in the hidden sectors through anomalies. We find these U(1) symmetries restrict the impact of small instantons in hidden sectors on the axion mass. Our study provides crucial insights into the dynamics within the CAA models and suggests broader implications for understanding small instanton effects in other composite axion models.

hep-ph↗

arXiv2024

Revisiting Metastable Cosmic String Breaking

Metastable cosmic strings appear in models of new physics with a two-step symmetry breaking $G\to H\to 1$, where $π_1(H)\neq 0$ and $π_1(G)=0$. They decay via the monopole-antimonopole pair creation inside. Conventionally, the breaking rate has been estimated by an infinitely thin string approximation, which requires a large hierarchy between the symmetry breaking scales. In this paper, we reexamine it by taking into account the finite sizes of both the cosmic string and the monopole. We obtain a robust lower limit on the tunneling factor $e^{-S_B}$ even for regimes the conventional estimate is unreliable. In particular, it is relevant to the cosmic string interpretation of the gravitational wave signals recently reported by pulsar timing array experiments.

hep-ph↗

arXiv2024

Navier--Stokes flow in the exterior of a moving obstacle with a Lipschitz boundary

Consider the three-dimensional Navier--Stokes flow past a moving rigid body $\mathscr{O} \subset \mathbb{R}^3$ with prescribed translational and angular velocities, where $\mathscr{O}$ stands for a bounded Lipschitz domain. We prove that the solution to the linearized problem is governed by a $C_0$-semigroup on solenoidal $L^q$-vector spaces with the $L^q$-$L^r$ estimates provided that $|1/q-1/2|<1/6+\varepsilon$ with some $\varepsilon>0$, where $r \ge q$ may be taken arbitrary large. As an application, we prove the existence and uniqueness of global mild solutions to the Navier--Stokes problem if the translational and angular velocities as well as the initial are sufficiently small.

math.AP↗

arXiv2023

Maximal $L_1$-regularity of the Navier-Stokes equations with free boundary conditions via a generalized semigroup theory

This paper develops a new approach to show the maximal regularity theorem of the Stokes equations with free boundary conditions in the half-space $\mathbb R^d_+$, $d \ge 2$, within the $L_1$-in-time and $\mathcal B^s_{q, 1}$-in-space framework with $(q, s)$ satisfying $1 < q < \infty$ and $1 + 1 / q < s < 1 / q$, where $\mathcal B^s_{q, 1}$ stands for either homogeneous or inhomogeneous Besov spaces. In particular, we establish a generalized semigroup theory within an $L_1$-in-time and $\mathcal B^s_{q,1}$-in-space framework, which extends a classical $C_0$-analytic semigroup theory to the case of inhomogeneous boundary conditions. The maximal $L_1$-regularity theorem is proved by estimating the Fourier--Laplace inverse transform of the solution to the generalized Stokes resolvent problem with inhomogeneous boundary conditions, where density and interpolation arguments are used. The maximal $L_1$-regularity theorem is applied to show the unique existence of a local strong solution to the Navier--Stokes equations with free boundary conditions for arbitrary initial data $\boldsymbol a$ in $B^s_{q, 1} (\mathbb R^d_+)^d$, where $q$ and $s$ satisfy $d-1 < q \le d$ and $-1+d/q < s < 1/q$, respectively. If we assume that the initial data $\boldsymbol a$ are small in $\dot B^{1 + d / q}_{q, 1} (\mathbb R^d_+)^d$, $d 1 < q < 2 d$, then the unique existence of a global strong solution to the system is proved.

math.AP↗

arXiv2022

More on Fake GUT

It is remarkable that the matter fields in the Standard Model (SM) are apparently unified into the $\mathrm{SU}(5)$ representations. A straightforward explanation of this fact is to embed all the SM gauge groups into a simple group containing $\mathrm{SU}(5)$, i.e., the grand unified theory (GUT). Recently, however, a new framework "fake GUT" has been proposed. In this new framework, the apparent matter unification can be explained by a chiral gauge group $G$, $ G \supset \mathrm{SU}(5)$. We emphasize that the SM matter fields are not necessarily embedded into the chiral representations to explain the apparent unification. In this paper, we discuss details of concrete realizations of the fake GUT model. We first study the model based on $\mathrm{SU}(5) \times \mathrm{U}(2)_H$, where $\mathrm{SU}(3)_c$ in the SM is from $\mathrm{SU}(5)$ while $\mathrm{SU}(2)_L\times \mathrm{U}(1)_Y$ are from the diagonal subgroups of $\mathrm{SU}(5) \times \mathrm{U}(2)_H$. We also extend this model to the one based on a semi-simple group, $\mathrm{SU}(5) \times \mathrm{SU}(3)_H$, so that $\mathrm{U}(2)_H$ is embedded in $\mathrm{SU}(3)_H$. We also show that this framework predicts rather different decay patterns of the proton, compared to the conventional GUT.

hep-ph↗

arXiv2021

Chiral Composite Asymmetric Dark Matter

The asymmetric dark matter (ADM) scenario solves the baryon-dark matter coincidence problem when the dark matter (DM) mass is of $\mathcal{O}(1)$GeV. Composite ADM models based on QCD-like strong dynamics are particularly motivated since the strong dynamics naturally provides the DM mass of $\mathcal{O}(1)$GeV and the large annihilation cross-section simultaneously. In those models, the sub-GeV dark photon often plays an essential role in transferring the excessive entropy in the dark sector into the visible sector, i.e., the Standard Model sector. This paper constructs a chiral composite ADM model where the $U(1)_D$ gauge symmetry is embedded into the chiral flavor symmetry. Due to the dynamical breaking of the chiral flavor symmetry, the model naturally provides the masses of the dark photon and the dark pions in the sub-GeV range, both of which play crucial roles for a successful ADM model.

hep-ph↗

arXiv2021

Global solvability of compressible-incompressible two-phase flows with phase transitions in bounded domains

Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains $Ω_{t +}, Ω_{t -} \subset \mathbb{R}^N$, $N \ge 2$, where the domains are separated by a sharp compact interface $Γ_t \subset \mathbb{R}^{N - 1}$. We prove a global in time unique existence theorem for such free boundary problem under the assumption that the initial data are sufficiently small and the initial domain of the incompressible fluid is close to a ball. In particular, we obtain the solution in the maximal $L_p - L_q$-regularity class with $2 < p <\infty$ and $N < q < \infty$ and exponential stability of the corresponding analytic semigroup on the infinite time interval.

math.AP↗

arXiv2021

Local well-posedness of incompressible viscous fluids in bounded cylinders with $90^\circ$-contact angle

We consider a free boundary problem of the Navier--Stokes equations in the three-dimensional Euclidean space with moving contact line, where the 90$^\circ$-contact angle condition is posed. We show that for given $T > 0$ the problem is local well-posed on $(0, T)$ provided that the initial data are small. In contrast to the strategy in Wilke (2013), we study the transformed problem in an $L^p$-in-time and $L^q$-in-space setting, which yields the optimal regularity of the initial data.

math.AP↗

arXiv2020

Strong solutions to compressible-incompressible two-phase flows with phase transitions

We consider a free boundary problem of compressible-incompressible two-phase flows with phase transitions in general domains of $N$-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The compressible fluid and the incompressible fluid are separated by either compact or non-compact sharp moving interface, and the surface tension is taken into account. In our model, the compressible fluid and incompressible fluid are occupied by the Navier-Stokes-Korteweg equations and the Navier-Stokes equations, respectively. This paper shows that for given $T > 0$ the problem admits a unique strong solution on $(0,T)$ in the maximal $L_p - L_q$ regularity class provided the initial data are small in their natural norms.

math.AP↗

arXiv2019

Global existence of the Navier-Stokes-Korteweg equations with a non-decreasing pressure in $\mathrm{L}^p$-framework

We consider the isentropic Navier-Stokes-Korteweg equations with a non-decreasing pressure on the whole space $\mathbb{R}^n$ $(n \ge 2)$, where the system describes the motion of compressible fluids such as liquid-vapor mixtures with phase transitions including a variable internal capillarity effect. We prove the existence of a unique global strong solution to the system in the $\mathrm{L}^p$-in-time and $\mathrm{L}^q$-in-space framework, especially in the maximal regularity class, by assuming $(p, q) \in (1, 2) \times (1, \infty)$ or $(p, q) \in \{2\} \times (1, 2]$. We show that the system is globally well-posed for small initial data belonging to $\mathrm{H}^{s + 1, q} (\mathbb{R}^n) \times \mathrm{H}^{s, q} (\mathbb{R}^n)^n$ provided $s > n/q$ if $q \le n$ and $s \ge 1$ if $q > n$. Our results allow the case when the derivative of the pressure is zero at a given constant state, that is, the critical states that the fluid changes a phase from vapor to liquid or from liquid to vapor. The arguments in this paper do not require any exact expression or a priori assumption on the pressure.

math.AP↗

arXiv2019

The Navier--Stokes equations in exterior Lipschitz domains: $\mathrm{L}^p$-theory

We show that the Stokes operator defined on $\mathrm{L}^p_σ (Ω)$ for an exterior Lipschitz domain $Ω\subset \mathbb{R}^n$ $(n \geq 3)$ admits maximal regularity provided that $p$ satisfies $| 1/p - 1/2| < 1/(2n) + \varepsilon$ for some $\varepsilon > 0$. In particular, we prove that the negative of the Stokes operator generates a bounded analytic semigroup on $\mathrm{L}^p_σ(Ω)$ for such $p$. In addition, $\mathrm{L}^p$-$\mathrm{L}^q$-mapping properties of the Stokes semigroup and its gradient with optimal decay estimates are obtained. This enables us to prove the existence of mild solutions to the Navier--Stokes equations in the critical space $\mathrm{L}^{\infty} (0 , T ; \mathrm{L}^3_σ (Ω))$ (locally in time and globally in time for small initial data).

math.AP↗