arXiv subjects

Nilasis Chaudhuri

Publications and source records attributed to Nilasis Chaudhuri.

At least 19 recordsLinked to original sources

arXiv2026

Dissipative measure-valued solutions and weak--strong uniqueness for a viscous Baer--Nunziato system with pressure relaxation

We study a viscous one-velocity Baer--Nunziato system for two barotropic compressible fluids in a bounded three-dimensional domain. In contrast with models in which the volume fraction is merely transported or determined by an algebraic equilibrium constraint, it satisfies a differential closure driven by the pressure gap between the phases. For arbitrary finite-energy initial data and adiabatic exponents $γ^\pm>1$, we construct global-in-time dissipative measure-valued solutions and prove dissipative measure-valued--strong uniqueness relative to any sufficiently regular solution with the same initial data. The principal difficulties are the singular and non-continuous behavior of the pressure-relaxation source at vanishing volume fractions, the associated concentration defects, and the lack of direct coercivity of the standard thermodynamic relative energy with respect to the volume fraction. These are resolved by an endpoint cutoff argument and an augmented relative energy coupled to the renormalized volume-fraction equation.

math.AP↗

arXiv2026

Generalized solution and Weak-Strong uniqueness for a barotropic Euler-Riesz system

We study the Euler--Riesz system on the torus $\mathbb T^d$, $d=2,3$: the compressible Euler equations with barotropic pressure $p(\varrho)=a\varrho^γ$ ($γ>1$, $a>0$), coupled to a repulsive nonlocal force ($\approx \varrho \nabla_x K \ast \varrho$) with Riesz kernel $K(x)\propto|x|^{β-d}$ of order $β\in(0,2)$. Since $K$ is the kernel of the inverse fractional Laplacian $(-Δ)^{-β/2}$, we recast the force through the Caffarelli--Silvestre extension as the trace of a local stress tensor, replacing the nonlocal interaction by a local identity in one extra variable. For a repulsive kernel the total energy is coercive, and we use this to introduce a notion of global-in-time \emph{dissipative solution} for arbitrarily large finite-energy data. Our main result is weak (measure-valued)--strong uniqueness, for every order $β\in(0,2)$ and every $γ>1$ independently: on any interval on which a strong solution exists, every dissipative solution with the same initial data coincides with it and all defects vanish. The proof rests on a suitable adaptation of relative energy.

math.AP↗

arXiv2026

Homogenization of compressible Navier-Stokes equations under a hard sphere pressure law

We consider the compressible time-dependent Navier-Stokes equations in a bounded perforated domain in dimensions two and three. Provided the perforations are small enough, we show that the limiting equations do not change their form when the perforation size goes to zero while their number increases to infinity. The novelty of this result is the form of the pressure: we consider a hard-sphere pressure law, giving an \emph{a priori} bound for the density while, compared to the barotropic case, having worse regularity for the pressure, therefore causing significant problems in the homogenization procedure. To the best of our knowledge, the homogenization for this kind of pressures has not been addressed in the literature yet.

math.AP↗

arXiv2025

Weak-Strong Uniqueness and Relaxation Limit for a Navier-Stokes-Korteweg Model

We consider a parabolic relaxation model for the compressible Navier-Stokes-Korteweg equations in the isothermal framework. This system depends on the relaxation parameters $α,β>0$ and approximates formally solutions of the compressible Navier-Stokes-Korteweg equations in the relaxation limit $α\to \infty$ and $β\to 0$. Introducing the class of finite energy weak solutions for the initial-boundary value problem corresponding to the relaxation model in spatial dimension three, we show that the weak-strong uniqueness principle holds. It asserts that a weak solution and a strong solution emanating from the same initial data coincide as long as the strong solution exists. Furthermore, we contribute a rigorous convergence result for the relaxation limit $α\to \infty$ and $β\to 0$ and thus justify the relaxation model as an approximate model for the compressible Navier-Stokes-Korteweg equations from a mathematical point of view. Our results hold for general non-monotone pressure-density relations.

math.AP↗

arXiv2025

Anelastic approximation for the degenerate compressible Navier--Stokes equations revisited

In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of $κ$-entropy, we rigorously justify the convergence of weak solutions toward the generalized anelastic system in a three-dimensional periodic domain for well-prepared initial data. For general ill-prepared initial data, we establish a similar convergence result in the whole space, relying essentially on dispersive estimates for acoustic waves. Compared with the work of Fanelli and Zatorska [Commun. Math. Phys., 400 (2023), pp. 1463-1506], our analysis is conducted for the standard isentropic pressure law, thereby eliminating the need for the cold pressure term that played a crucial role in the previous approach. To the best of our knowledge, this is the first rigorous singular limit result for the compressible Navier-Stokes equations with degenerate viscosity that requires no additional regularization of the system.

math.AP↗

arXiv2024

Regular solutions to the dissipative Aw-Rascle system

In this paper we prove the local-in-time existence of regular solutions to dissipative Aw-Rascle system with the offset equal to gradient of some increasing and regular function of density. It is a mixed degenerate parabolic-hyperbolic hydrodynamic model, and we extend the techniques previously developed for compressible Navier-Stokes equations to show the well-posedness of the system in the $L_2-L_2$ setting. We also discuss relevant existence results for offset involving singular or nonlocal functions of density.

math.AP↗

arXiv2024

Construction of weak solutions to the equations of a compressible viscous model

The paper aims on the construction of weak solutions to equations of a model of compressible viscous fluids, being a simplification of the classical compressible Navier-Stokes system. We present a novel scheme for approximating systems that preserves structural integrity by avoiding classical regularization with $ - \varepsilon Δ\varrho $, thus maintaining the transport character of the continuity equation. Our approach, which necessitates specific conditions on the constitutive equation, accommodates physically relevant models such as isentropic and van der Waals gases, and globally handles non-monotone pressures. From an analytical perspective, our method synthesizes techniques from Feireisl-Lions and Bresch-Jabin to demonstrate the convergence of approximate densities using compensated compactness techniques. We also apply renormalization of the continuity equations and utilize weight techniques to manage unfavorable terms.

math.AP↗

arXiv2024

Local existence and conditional regularity for the Navier-Stokes-Fourier system driven by inhomogeneous boundary conditions

We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional regularity we mean that any strong solution belonging to a suitable class remains regular as long as its amplitude remains bounded. The result holds for general Dirichlet-Neumann boundary conditions provided the material derivative of the velocity field vanishes on the boundary of the physical domain. As a corollary of this result we obtain: Blow up criteria for strong solutions, Local existence of strong solutions in the optimal L^p-L^q framework, Alternative proof of the existing results on local well posedness.

math.AP↗

arXiv2024

Non-local dissipative Aw-Rascle model and its relation with Matrix-valued communication in Euler alignment

We compare the multi-dimensional generalisation of the Aw-Rascle model with the pressureless Euler-alignment system, in which the communication weight is matrix-valued. Our generalisation includes the velocity offset in the form of a gradient of a non-local density function, given by the convolution with a kernel $K$. We investigate connections between these models at the macroscopic, mesoscopic and macroscopic (hydrodynamic) level, and overview the results on the mean-field limit for various assumptions on $K$.

math.AP↗

arXiv2024

On thermally driven fluid flows arising in astrophysics

We consider the Navier-Stokes-Fourier-Poisson system driven by an inhomogeneous temperature distribution on the boundary of an exterior fluid domain. We impose the finite mass constraint, positive far field condition for the temperature as well as the no--slip boundary conditions for the velocity. The existence of global--in--time weak solutions and the weak-strong principle are proved.

math.AP↗

arXiv2024

Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system

We introduce the notion of duality solution for the hard-congestion model on the real line, and additionally prove an existence result for this class of solutions. Our study revolves around the analysis of a generalised Aw-Rascle system, where the offset function is replaced by the gradient of a singular function, such as $ρ$ $γ$ n , where $γ$ $\rightarrow$ $\infty$. We prove that under suitable assumptions on the initial data, solutions to the Aw-Rascle system converge towards the so-called duality solutions, which have previously found applications in other systems which exhibit compressive dynamics. We also prove that one can obtain weak solutions to the limiting system under stricter assumptions on the initial data. Finally, we discuss (non-)uniqueness issues.

math.AP↗

arXiv2024

Low Mach number limit on perforated domains for the evolutionary Navier-Stokes-Fourier system

We consider the Navier-Stokes-Fourier system describing the motion of a compressible, viscous and heat-conducting fluid on a domain perforated by tiny holes. First, we identify a class of dissipative solutions to the Oberbeck-Boussinesq approximation as a low Mach number limit of the primitive system. Secondly, by proving the weak-strong uniqueness principle, we obtain strong convergence to the target system on the lifespan of the strong solution.

math.AP↗

arXiv2024

Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming

We consider a one-dimensional hydrodynamic model featuring nonlocal attraction-repulsion interactions and singular velocity alignment. We introduce a two-velocity reformulation and the corresponding energy-type inequality, in the spirit of the Bresch-Desjardins estimate. We identify a dependence between the communication weight and interaction kernel and between the pressure and viscosity term allowing for this inequality to be uniform in time. It is then used to study long-time asymptotics of solutions.

math.AP↗

arXiv2023

On a blow-up criterion for the Navier-Stokes-Fourier system under general equations of state

In this paper we prove a blow-up criterion for the compressible Navier-Stokes-Fourier system for general thermal and caloric equations of state with inhomogeneous boundary conditions for the velocity and the temperature. Assuming only that Gibb's equation and the thermodynamic stability hold, we show that solutions in a certain regularity class remain regular under the condition that the density, the temperature and the modulus of the velocity are bounded.

math.AP↗

arXiv2023

Analysis of the generalised Aw-Rascle model

We consider the multi-dimensional generalization of the Aw-Rascle system for vehicular traffic. For an arbitrary large class of initial data and the periodic domain, we prove the existence of global-in-time measure-valued solutions. Moreover, using the relative energy technique, we show that the measure-valued solutions coincide with the classical solutions as long as the latter exist.

math.AP↗

arXiv2023

A new construction of weak solutions to compressible Navier-Stokes equations

We prove the existence of the weak solutions to the compressible Navier--Stokes system with barotropic pressure $p(\varrho)=\varrho^γ$ for $γ\geq 9/5$ in three space dimension. The novelty of the paper is the approximation scheme that instead of the classical regularization of the continuity equation (based on the viscosity approximation $\ep Δ\varrho$) uses more direct truncation and regularisation of nonlinear terms an the pressure. This scheme is compatible with the Bresch-Jabin compactness criterion for the density. We revisit this criterion and prove, in full rigour, that it can be applied in our approximation at any level.

math.AP↗

arXiv2022

Nonuniqueness of weak solutions to the dissipative Aw-Rascle model

We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a dissipation effect, similar to viscous dissipation in the compressible viscous fluid models. We show that despite this dissipation, the extension of the method of convex integration can be applied to generate infinitely many weak solutions connecting arbitrary initial and final states. We also show that for certain choice of data, ill posedness holds in the class of admissible weak solutions.

math.AP↗

arXiv2022

On weak(measure valued)-strong uniqueness for Navier-Stokes-Fourier system with Dirichlet boundary condition

In this paper, our goal is to define a measure valued solution of compressible Navier--Stokes--Fourier system for a heat conducting fluid with Dirichlet boundary condition for temperature in a bounded domain. The definition is based on the weak formulation of entropy inequality and ballistic energy inequality. Moreover, we obtain the weak(measure valued)-strong uniqueness property of this solution with the help of relative energy.

math.AP↗