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

Chaudhuri, Nilasis

doi:10.1016/j.nonrwa.2019.03.004

Cited by 9 publications

(11 citation statements)

References 15 publications

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“…Weak-Strong uniqueness principle for monotone pressure has been proved by Feireisl et al in [11] and [14] for weak solutions and in [10] for measure-valued solutions. Recently, weak-strong uniqueness principle in the class of weak solutions has been shown for the compressible Navier-Stokes system with a general non-monotone pressure density relation and/or the singular hard sphere pressure in [9] and [4] . To prove the above mentioned results the key tool is the presence of viscosity.…”

Section: Introductionmentioning

confidence: 99%

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On Weak (Measure-Valued)–Strong Uniqueness for Compressible Navier–Stokes System with Non-monotone Pressure Law

Chaudhuri

2020

J. Math. Fluid Mech.

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In this paper our goal is to define a renormalised dissipative measure-valued (rDMV) solution of compressible Navier-Stokes system for fluids with nonmonotone 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.• Pressure Law: In an isentropic setting, the pressure p and the density ̺ of the fluid are interrelated by :(1.4) Remark 1.1. The Consideration of h in (1.4) has been motivated from isentropic equation of state given by h(̺) = a̺ γ with γ ≥ 1 and a > 0.• Here we consider no slip boundary condition for velocity i.e. u| {∂Ω×(0,T )}=0 .( 1.5) The compressible Navier-Stokes equations admit global-in-time weak solution(s) for general finite energy initial data and a large class of pressure-density constitutive relations. Considering q ≡ 0 in (1.4) and following the literatures of Antontsev et al.[1], Lions[15], Feireisl[8], Plotnikov et al.[18] and many others, we observe globalin-time weak solution for adiabatic exponent γ ≥ 1 for d = 1, 2 and γ > 3 2 for d = 3. Even for non-monotone pressure, Feireisl in [7] has proved a similar result and recent work by Bresch and Jabin [2] indicates that for p ∈ C 1 [0, ∞) ≥ 0, p(0) = 0, lim ̺→∞ p ′ (̺) ̺ γ−1 = a > 0 and γ ≥ 2 the system admits a weak solution. So it may seem unnecessary to develop the theory of measure valued solution that extends the class of generalised solutions but in the following discussion we will try to justify why we still choose to consider it.

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Section: Introductionmentioning

confidence: 99%

“…To deal with the non-monotone pressure in Feireisl [9] and [4] the use of the renormalized version of the equation of continuity plays a crucial role. But that is non-linear with respect to the velocity gradient and density.…”

Section: Introductionmentioning

confidence: 99%

On Weak (Measure-Valued)–Strong Uniqueness for Compressible Navier–Stokes System with Non-monotone Pressure Law

Chaudhuri

2020

J. Math. Fluid Mech.

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“…We would like to point out that (5) allows the pressure to be a general non-monotone function of the density, besides the standard case p( ) = a γ with a > 0 and γ > N 2 . Still, as we shall see below, the problem admits global-intime weak solutions and retains other fundamental properties of the system, notably the weak-strong uniqueness, see [5].…”

Section: Introductionmentioning

confidence: 94%

Semiflow selection for the compressible Navier–Stokes system

Basarić

2020

J. Evol. Equ.

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Although the existence of dissipative weak solutions for the compressible Navier–Stokes system has already been established for any finite energy initial data, uniqueness is still an open problem. The idea is then to select a solution satisfying the semigroup property, an important feature of systems with uniqueness. More precisely, we are going to prove the existence of a semiflow selection in terms of the three state variables: the density, the momentum, and the energy. Finally, we will show that it is possible to introduce a new selection defined only in terms of the initial density and momentum; however, the price to pay is that the semigroup property will hold almost everywhere in time.

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“…By means of the relative entropy method, Feireisl et al not only proved the weak-strong uniqueness of finiteenergy weak solution to compressible Navier-Stokes equations with monotone pressure in [8], but also proved the weak-strong uniqueness property for compressible Naiver-Stokes equations with non-monotone pressure in [9]. When the pressure function satisfies a hard sphere law, the weakstrong uniqueness of Navier-Stokes equations is established by Feireisl et al in [10] and Chaudhur in [11] applying the method of relative entropy.…”

Section: Introductionmentioning

confidence: 99%

Weak-Strong Uniqueness for Compressible Magnetohydrodynamic Equations with Coulomb Force

Zhou

2021

Advances in Mathematical Physics

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

Cited by 9 publications

References 15 publications

On Weak (Measure-Valued)–Strong Uniqueness for Compressible Navier–Stokes System with Non-monotone Pressure Law

On Weak (Measure-Valued)–Strong Uniqueness for Compressible Navier–Stokes System with Non-monotone Pressure Law

Semiflow selection for the compressible Navier–Stokes system

Weak-Strong Uniqueness for Compressible Magnetohydrodynamic Equations with Coulomb Force

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