Searcharxiv⌕ Search

arXiv subjects

Huali Zhang

Publications and source records attributed to Huali Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Low regularity solutions for the Cauchy problem of the ideal incompressible Magnetohydrodynamics equations

In Lagrangian coordinates, the local well-posedness of low regularity solutions is established for an ideal incompressible magnetohydrodynamic (MHD) system subject to a homogeneous background magnetic field. First, the MHD system is reformulated into a degenerate wave-elliptic system with a particular null structure. By introducing a suitably defined solution space, several refined product estimates are derived. Next, using the inherent null structure, a Klainerman-Machedon type bilinear estimate is obtained for the nonlinear terms. These nice structures and estimates yield the local well-posedness of the ideal incompressible MHD equations in Lagrangian coordinates for initial velocity fields $\bv_0 \in H^{s}(\mathbb{R}^n)$ with $s > \frac{n+1}{2}$ $(n=2,3,4)$. Moreover, the regularity requirement is lowered by half a derivative compared with the classical exponent $s > \frac{n}{2}+1$.

math.AP↗
arXiv2026

Almost optimal well-posedness for Chern--Simons gauged $O(3)$ sigma model under the Lorenz gauge

In this paper, we study the low-regularity Cauchy problem for the Chern--Simons gauged $O(3)$ sigma model in $\mathbb{R}^{1+d}$ ($d=1,2$) under the Lorenz gauge. For $d=1$, we establish local well-posedness for initial data $(\boldsymbolϕ_0,\mathbf{A}_0)\in H^{s_1}(\mathbb{R})\times H^{s_1-1}(\mathbb{R})$ with $s_1>\frac12$. This improves the previous result of Jin and Huh \cite{HJ} by one quarter of a derivative and is almost optimal in view of the scaling-invariant regularities $\dot H^{1/2}(\mathbb{R})$ for the matter field and $\dot H^{-1/2}(\mathbb{R})$ for the gauge field. For $d=2$, we establish local well-posedness for initial data $(\boldsymbolϕ_0,\mathbf{A}_0)\in H^{s_2}(\mathbb{R}^2)\times H^{s_2-\frac34}(\mathbb{R}^2)$ with $s_2>1$. This improves the previous result of Jin and Zhang \cite{JZ} by one quarter of a derivative and brings the regularity threshold close to the scaling-invariant exponents $\dot H^{1}(\mathbb{R}^2)$ and $\dot H^{0}(\mathbb{R}^2)$ for the matter and gauge fields, respectively. The analysis relies on two main ingredients. In two space dimensions, we identify the complete null structure of the derivative nonlinearities, allowing the entire system to be treated within a unified null-form framework. In one space dimension, we establish a direct energy estimate in the function space introduced by Keel and Tao, avoiding the finite-propagation reduction to a small-data problem and enabling the low-regularity iteration for general initial data.

math.AP↗
arXiv2026

Well-posedness for rough solutions of the 3D compressible Euler equations

In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity $(\mathbf{v}_0, ρ_0, \mathbf{w}_0) \in H^{2+} \times H^{2+} \times H^{2}$, improving on the regularity conditions of \cite{WQEuler}. The continuous dependence on initial data for rough solutions of the compressible Euler system is new, even with the same regularity conditions as in \cite{WQEuler}. In addition, we prove new local well-posedness results for the 3D compressible Euler system with entropy.

math.AP↗
arXiv2025

Low Regularity Well-Posedness of Cauchy Problem for Two-Dimensional Relativistic Euler Equation

In this article, we initiate the study of the Cauchy problem for the two-dimensional relativistic Euler equations in a low-regularity setting. By introducing good variables--a rescaled velocity, logarithmic enthalpy, and an appropriately defined vorticity, we reformulate the equations into a coupled wave-transport system. First, we prove the existence and uniqueness of solutions when the initial logarithmic enthalpy $h_0$, rescaled velocity $\bv_0$, and vorticity $\bw_0$ satisfy $(h_0, \bv_0, \bw_0, \nabla \bw_0) \in H^{\frac{7}{4}+}(\mathbb{R}^2) \times H^{\frac{7}{4}+}(\mathbb{R}^2) \times H^{\frac32+}(\mathbb{R}^2) \times L^8(\mathbb{R}^2)$. By using Strichartz estimates and semiclassical analysis, a relaxed well-posedness result holds when $(h_0, \bv_0, \bw_0, \nabla \bw_0) \in H^{\frac{7}{4}+}(\mathbb{R}^2) \times H^{\frac{7}{4}+}(\mathbb{R}^2) \times H^{\frac32}(\mathbb{R}^2) \times L^8(\mathbb{R}^2)$. Both results are valid for the general state function $p(\varrho)=\varrho^A$ ($A \geq 1$). Secondly, in the special case where $p(\varrho)=\varrho$, the acoustic metric reduces to the standard flat Minkowski metric. We can establish the well-posedness of solutions when $(h_0, \mathbf{v}_0, \mathbf{w}_0) \in H^{\frac{7}{4}+}(\mathbb{R}^2) \times H^{\frac{7}{4}+}(\mathbb{R}^2) \times H^{1+}(\mathbb{R}^2)$. The regularity exponents for the log-enthalpy and rescaled velocity correspond to those in Smith and Tataru \cite{ST}, while the vorticity regularity corresponds to Bourgain and Li \cite{BL}. Moreover, if the stiff flow is irrotational, we can prove the local well-posedness for $(h_0, \mathbf{v}_0) \in H^{1+}(\mathbb{R}^2)$, and global well-posedness for small initial data $(h_0, \bv_0) \in \dot{B}^{1}_{2,1}(\mathbb{R}^2)$.

math.AP↗
arXiv2025

Improved Local Well-Posedness in Sobolev Spaces for Two-Dimensional Compressible Euler Equations

We establish the local existence and uniqueness of solutions to the two-dimensional compressible Euler equations with initial velocity $\bv_0$, logarithmic density $ρ_0$, and specific vorticity \(w_0\), which satisfy $(\bv_0, ρ_0, w_0, \nabla w_0)\in H^{\frac74+}(\mathbb{R}^2)\times H^{\frac74+}(\mathbb{R}^2) \times H^{\frac32}(\mathbb{R}^2) \times L^{8}(\mathbb{R}^2)$. The proof applies Smith-Tataru method \cite{ST} and the inherent wave-transport structure of the two-dimensional compressible Euler equations. The key observation is that Strichartz estimates hold when the regularity requirement for vorticity is lower than that for velocity and density, even though the gradient of vorticity appears as a source term in the velocity wave equation. Furthermore, our result presents an improvement of $\frac{1}{4}$-order regularity compared to previous results \cite{Z1} and \cite{Z2}.

math.AP↗
arXiv2025

Low regularity solutions of two-dimensional compressible Euler equations with dynamic vorticity

By establishing a sharp Strichartz estimate for the velocity and density, we prove the local well-posedness of solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial velocity, density, and specific vorticity $(\bv_0, ρ_0, \varpi_0) \in H^{s}(\mathbb{R}^2)\times H^{s}(\mathbb{R}^2) \times H^2(\mathbb{R}^2), s>\frac{7}{4}$. Our strategy relies on Smith-Tataru's work \cite{ST} for quasi-linear wave equations.

math.AP↗
arXiv2025

Local well-posedness for Chern-Simons gauged $O(3)$ sigma equations under the Lorenz gauge

In this paper, we study the Cauchy problem for the Chern-Simons gauged $O(3)$ sigma model under the Lorenz gauge condition. We prove the local well-posedness of solutions if the initial matter field and gauge field satisfy $(\bmϕ_0, \bA_0) \in H^s(\R^2)\times H^{s-\frac12}(\R^2)$, $s>1$, where the critical regularity for $\bmϕ_0$ is $s_c=1$. Our proof is based on identifying null forms within the system and utilizing bilinear estimates in wave-Sobolev space.

math.AP↗
arXiv2025

Orientation-dependent superconductivity and electronic structure of the rare-earth metal/KTaO3 interfaces

The recent discovery of orientation-dependent superconductivity in KTaO3-based interfaces has attracted considerable interest, while the underlying origin remains an open question. Here we report a different approach to tune the interfacial electron gas and superconductivity by forming interfaces between rare-earth (RE) metals (RE being La, Ce, Eu) and KTaO3 substrates with different orientations. We found that the interfacial superconductivity is strongest for the Eu/KTaO3 interfaces, becomes weaker in La/KTaO3 and is absent in Ce/KTaO3. Using in-situ photoemission, we observed distinct valence bands associated with RE metals, as well as a pronounced orientation dependence in the interfacial electronic structure, which can be linked to the orientation-dependent superconductivity. The photoemission spectra show similar double-peak structures for the (111) and (110) oriented interfaces, with an energy separation close to the LO4 phonon of KTaO3. Detailed analyses suggest that this double-peak structure could be attributed to electron-phonon coupling, which might be important for the interfacial superconductivity.

cond-mat.supr-con↗
arXiv2024

Strichartz estimates and low regularity solutions of 3D relativistic Euler equations

We study the low regularity well-posedness for Cauchy problem of 3D relativistic Euler equations. Firstly, we introduce a new decomposition for relativistic velocity and derive new transport equations for vorticity, which both play a crucial role in energy and Strichartz estimates. According to Smith-Tataru's approach, we then establish a Strichartz estimate of linear wave equations endowed with the acoustic metric. This leads us to prove a complete local well-posedness result if the initial logarithmic enthalpy, velocity, and modified vorticity $(h_0, \bu_0, \bw_0) \in H^s \times H^s \times H^{s_0} (2<s_0<s)$. Therefore, we give an affirmative answer to "Open Problem D" proposed by Disconzi. Moreover, for $(h_0,{\bu}_0,\bw_0) \in H^{2+} \times H^{2+} \times H^2$, by frequency truncation, there is a stronger Strichartz estimate for solutions on a short-time-interval. By semi-classical analysis and induction method, these solutions can be extended from short time intervals to a regular time interval, and a uniform Strichartz estimate with loss of derivatives can be obtained. This allows us to prove the local well-posedness of 3D relativistic equations if $(h_0,{\bu}_0,\bw_0) \in H^{2+} \times H^{2+} \times H^2$.

math.AP↗
arXiv2024

Local well-posedness for incompressible neo-Hookean Elastic equations in almost critical Sobolev spaces

Inspired by a pioneer work of Andersson-Kapitanski \cite{AK}, we prove the local well-posedness of the Cauchy problem of incompressible neo-Hookean equations if the initial deformation and velocity belong to $H^{s+1}(\mathbb{R}^n) \times H^{s}(\mathbb{R}^n), s>\frac{n+1}{2}$ ($n=2,3$). Moreover, if the initial data is small, then we can lower the regularity to $s>\frac{n}{2}$, where $\frac{n+2}{2}$ and $\frac{n}{2}$ is respectively a scaling-invariant exponent for deformation and velocity in Sobolev spaces. Our new observation relies on two folds: a reduction to a second-order wave-elliptic system of deformation and velocity; and a "wave-map type" null form intrinsic in this coupled system. In particular, the wave nature with "wave-map type" null form allows us to prove a bilinear estimate of Klainerman-Machedon type for nonlinear terms. So we can lower $\frac12$-order regularity in 3D and $\frac34$-order regularity in 2D for well-posedness compared with \cite{AK}.

math.AP↗
arXiv2024

Fermi Surface Nesting with Heavy Quasiparticles in the Locally Noncentrosymmetric Superconductor CeRh$_2$As$_2$

The locally noncentrosymmetric heavy fermion superconductor CeRh$_2$As$_2$ has attracted considerable interests due to its rich superconducting phases, accompanied by a quadrupole density wave and pronounced antiferromagnetic excitations. To understand the underlying physics, we here report measurements from high-resolution angle-resolved photoemission. Our results reveal fine splittings of the conduction bands related to the locally noncentrosymmetric structure, as well as a quasi-two-dimensional Fermi surface (FS) with strong $4f$ contributions. The FS exhibits nesting with an in-plane vector $(π/a, π/a)$, which is facilitated by the van Hove singularity near $\bar X$ that arises from the characteristic conduction-$f$ hybridization. The FS nesting provides a natural explanation for the observed antiferromagnetic excitations at $(π/a, π/a)$, which could be intimately connected to its unconventional superconductivity. Our experimental results are well supported by density functional theory plus dynamical mean field theory calculations, which can capture the strong correlation effects. Our study not only provides spectroscopic proof of the key factors underlying the field-induced superconducting transition, but also uncovers the critical role of FS nesting and lattice Kondo effect in the intertwined spin and charge fluctuations.

cond-mat.str-el↗
arXiv2023

Electronic band reconstruction across the insulator-metal transition in colossal magnetoresistive EuCd2P2

While colossal magnetoresistance (CMR) in Eu-based compounds is often associated with strong spin-carrier interactions, the underlying reconstruction of the electronic bands is much less understood from spectroscopic experiments. Here using angle-resolved photoemission, we directly observe an electronic band reconstruction across the insulator-metal (and magnetic) transition in the recently discovered CMR compound EuCd2P2. This transition is manifested by a large magnetic band splitting associated with the magnetic order, as well as unusual energy shifts of the valence bands: both the large ordered moment of Eu and carrier localization in the paramagnetic phase are crucial. Our results provide spectroscopic evidence for an electronic structure reconstruction underlying the enormous CMR observed in EuCd2P2, which could be important for understanding Eu-based CMR materials, as well as designing CMR materials based on large-moment rare-earth magnets.

cond-mat.mtrl-sci↗
arXiv2022

Quasiparticle characteristics of the weakly ferromagnetic Hund's metal MnSi

Hund's metals are multi-orbital systems with $3d$ or $4d$ electrons exhibiting both itinerant character and local moments, and they feature Kondo-like screenings of local orbital and spin moments, with suppressed coherence temperature driven by Hund's coupling $J_H$. They often exhibit magnetic order at low temperature, but how the interaction between the Kondo-like screening and long-range magnetic order is manifested in the quasiparticle spectrum remains an open question. Here we present spectroscopic signature of such interaction in a Hund's metal candidate MnSi exhibiting weak ferromagnetism. Our photoemission measurements reveal renormalized quasiparticle bands near the Fermi level with strong momentum dependence: the ferromagnetism manifests through possibly exchange-split bands (Q1) below $T_C$ , while the spin/orbital screenings lead to gradual development of quasiparticles (Q2) upon cooling. Our results demonstrate how the characteristic spin/orbital coherence in a Hund's metal could coexist and compete with the magnetic order to form a weak itinerant ferromagnet, via quasiparticle bands that are well separated in momentum space and exhibit distinct temperature dependence. Our results imply that the competition between the spin/orbital screening and the magnetic order in a Hund's metal bears intriguing similarity to the Kondo lattice systems.

cond-mat.str-el↗
arXiv2021

On the rough solutions of 3D compressible Euler equations: an alternative proof

The well-posedness of Cauchy problem of 3D compressible Euler equations is studied. By using Smith-Tataru's approach \cite{ST}, we prove the local existence, uniqueness and stability of solutions for Cauchy problem of 3D compressible Euler equations, where the initial data of velocity, density, specific vorticity $v, ρ\in H^s, \varpi \in H^{s_0} (2<s_0<s)$. It's an alternative and simplified proof of the result given by Q. Wang in \cite{WQEuler}.

math.AP↗
arXiv2021

Global large, smooth solutions of the 2D surface quasi-geostrophic equations

In this paper, we prove the global regularity of smooth solutions to 2D surface quasi-geostrophic (SQG) equations with super-critical dissipation for a class of large initial data, where the velocity and temperature can be arbitrarily large in spaces $L^\infty(\mathbb{R}^2)$ and $H^3(\mathbb{R}^2)$. This result could be seen as an improvement work of Liu-Pan-Wu \cite{Liu}, for it's without any smallness hypothesis of the $L^\infty(\mathbb{R}^2)$ norm of the initial data.

math.AP↗
arXiv2021

On 3D Hall-MHD equations with fractional Laplacians: global well-posedness

Cauchy problem for 3D incompressible Hall-magnetohydrodynamics (Hall-MHD) system with fractional Laplacians is studied. First, global well-posedness of small-energy solutions with general initial data in $H^s$, $s>\frac{5}{2}$, is proved. Second, a special class of large-energy initial data is constructed, with which the Cauchy problem is globally well-posed. The proofs rely upon a new global bound of energy estimates involving Littlewood-Paley decomposition and Sobolev inequalities, which enables one to overcome the $\frac{1}{2}$-order derivative loss of the magnetic field.

math.AP↗
arXiv2020

Blow up of fractional Schrödinger equations on manifolds with nonnegative Ricci curvature

In this paper, the well-posedness of Cauchy's problem of fractional Schrödinger equations with a power type nonlinearity on $n$-dimensional manifolds with nonnegative Ricci curvature is studied. Under suitable volume conditions, the local solution with initial data in $H^{[\frac{n}{2}]+1}$ will blow up in finite time no matter how small the initial data is, which follows from a new weight function and ODE inequalities. Moreover, the upper-bound of the lifespan can be estimated.

math.AP↗