arXiv subjects

Nilasis Chaudhuri

Publications and source records attributed to Nilasis Chaudhuri.

24 records · Page 2Linked to original sources

arXiv2021

Navier-Stokes-Fourier system with Dirichlet boundary conditions

We consider the Navier--Stokes--Fourier system describing the motion of a compressible, viscous, and heat conducting fluid in a bounded domain with general non-homogeneous Dirichlet boundary conditions for the velocity and the absolute temperature, with the associated boundary conditions for the density on the inflow part. We introduce a new concept of weak solution based on the satisfaction of the entropy inequality together with a balance law for the ballistic energy. We show the weak-strong uniqueness principle as well as the existence of global-in-time solutions.

math.AP↗

arXiv2020

Limit of a consistent approximation to the complete compressible Euler System

The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of compressible complete Euler system in the full space $ \mathbb{R}^d,\; d=2,3 $ is a weak solution of the system then eventually the approximate solutions converge strongly in suitable norms locally under a minimal assumption on the initial data of the approximate solutions. The class of consistent approximate solutions is quite general including the vanishing viscosity and heat conductivity limit. In particular, they may not satisfy the minimal principle for entropy.

math.AP↗

arXiv2019

Multiple scales and singular limits of perfect fluids

In this article our goal is to study the singular limits for a scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach number $=ε^m $, Rossby number $=ε$ and Froude number $=ε^n $ are proportional to a small parameter $ε\rightarrow 0$. The fluid is confined to an infinite slab, the limit behaviour is identified as the incompressible Euler system. For \emph{well--prepared} initial data, the convergence is shown on the life span time interval of the strong solutions of the target system, whereas a class of generalized \emph{dissipative solutions} is considered for the primitive system. The technique can be adapted to the compressible Navier--Stokes system in the subcritical range of the adiabatic exponent $γ$ with $1<γ\leq\frac{3}{2}$, where the weak solutions are not known to exist.

math.AP↗

arXiv2019

Singular limits for compressible inviscid rotating fluids

We study singular limit for scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach and Rossby numbers are proportional to a small parameter $ε$. If the fluid is confined to an infinite slab, the limit behaviour is identified as a horizontal motion of an incompressible inviscid system that is analogous to the Euler system. We consider a very general class of solutions, named dissipative solution for the scaled compressible Euler systems and will show that it converges to a strong solution of that incompressible inviscid system.

math.AP↗

arXiv2019

On weak (measure-valued)-strong uniqueness for compressible Navier-Stokes system with non-monotone pressure law

In this paper our goal is to define a renormalised dissipative measure--valued (rDMV) solution of compressible Navier--Stokes system for fluids with non-monotone pressure--density relation. We prove existence of rDMV solutions and establish a suitable relative energy inequality. Moreover we obtain the Weak (Measure-valued)-Strong uniqueness property of this rDMV solution with the help of relative energy inequality.

math.AP↗

arXiv2018

On weak-strong uniqueness for compressible Navier-Stokes system with general pressure laws

The goal of the present paper is to study the weak--strong uniqueness problem for the compressible Navier--Stokes system with a general barotropic pressure law. Our results include the case of a hard sphere pressure of Van der Waals type with a non--monotone perturbation and a Lipschitz perturbation of a monotone pressure. Although the main tool is the relative energy inequality, the results are conditioned by the presence of viscosity and do not seem extendable to the Euler system.

math.AP↗