Measure-valued solutions to the complete Euler system revisited

Březina, Jan; Feireisl, Eduard

doi:10.1007/s00033-018-0951-8

Cited by 21 publications

(26 citation statements)

References 24 publications

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“…Another example of such approximate problem may be derived from two models, Navier-Stokes-Fourier system and Brenner's Model. A discussion about these models have been presented in Březina and Feireisl [7]. Also in [20] and [22] the authors consider approximate solutions of the complete Euler system using numerical schemes (finite volume) motivated by the Brenner's model.…”

Section: (): V-volmentioning

confidence: 99%

“…The consistent approximations typically generate the so-called measure-valued solutions. For the complete Euler system existence of measure valued solutions has been proved by Březina and Feireisl [6,7] with the help of Young measures. Later in [5], Breit, Feireisl and Hofmanová define dissipative solutions for the same system, by modifying the measure-valued solutions suitably.…”

Section: (): V-volmentioning

confidence: 99%

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Limit of a Consistent Approximation to the Complete Compressible Euler System

Chaudhuri

2021

J. Math. Fluid Mech.

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The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of the compressible complete Euler system in full space $$ \mathbb {R}^d,\; d=2,3 $$ R d , d = 2 , 3 is a weak solution of the system, then the approximate solutions eventually 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 and includes the vanishing viscosity and heat conductivity limit. In particular, they may not satisfy the minimal principle for entropy.

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Section: (): V-volmentioning

confidence: 99%

Section: (): V-volmentioning

confidence: 99%

Limit of a Consistent Approximation to the Complete Compressible Euler System

Chaudhuri

2021

J. Math. Fluid Mech.

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“…The relative energy is a coercive functional (see. Bruell et al [9] and Březina and Feireisl [12]) satisfying the estimate…”

Section: Relative Energy Inequalitymentioning

confidence: 93%

Multiple scales and singular limits of perfect fluids

Chaudhuri

2022

J. Evol. Equ.

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In this article, our goal is to study the singular limits for a scaled barotropic Euler system modeling a rotating, compressible and inviscid fluid, where Mach number $$=\epsilon ^m $$ = ϵ m , Rossby number $$=\epsilon $$ = ϵ and Froude number $$=\epsilon ^n $$ = ϵ n are proportional to a small parameter $$\epsilon \rightarrow 0$$ ϵ → 0 . The fluid is confined to an infinite slab, the limit behavior is identified as the incompressible Euler system or a damped incompressible Euler system depending on the relation between m and n. For well-prepared initial data, the convergence is shown on the lifespan time interval of the strong solutions of the target system, whereas a class of generalized 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 $$\gamma $$ γ with $$1<\gamma \le \frac{3}{2}$$ 1 < γ ≤ 3 2 , where weak solutions are not known to exist.

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“…[14] We remark by passing that readers shall not be confused by the concept of measure solutions called in this paper (or measurevalued solutions called in [4]) with that of measure-valued solutions proposed by DiPerna. [7] The latter has been intensively studied recently (see, for example, [2,3] and references therein). Our measure solutions are measures supported on the physical space of independent variables, which describe, for example, concentration of mass etc.…”

Section: Introductionmentioning

confidence: 99%

Hypersonic limit of two‐dimensional steady compressible Euler flows passing a straight wedge

Yuan

Zhao

2020

Z Angew Math Mech

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We formulate a problem on hypersonic limit of two-dimensional steady non-isentropic compressible Euler flows passing a straight wedge. It turns out that the Mach number of the upcoming uniform supersonic flow increases to infinity may be taken as that the adiabatic exponent of the polytropic gas decreases to 1. We propose a form of the Euler equations which is valid if the unknowns are Radon measures and construct a measure solution containing Dirac measures supported on the surface of the wedge. It is proved that as → 1, the sequence of solutions of the compressible Euler equations that contains a shock ahead of the wedge converges vaguely as measures to the measure solution constructed. This justifies the Newton theory of hypersonic flow passing obstacles in the case of two-dimensional straight wedges. The result also demonstrates the necessity of considering general measure solutions in the study of boundary-value problems of systems of hyperbolic conservation laws. K E Y W O R D Scompressible Euler equations, Dirac measure, hypersonic, measure solution, shock wave, wedge

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Measure-valued solutions to the complete Euler system revisited

Cited by 21 publications

References 24 publications

Limit of a Consistent Approximation to the Complete Compressible Euler System

Limit of a Consistent Approximation to the Complete Compressible Euler System

Multiple scales and singular limits of perfect fluids

Hypersonic limit of two‐dimensional steady compressible Euler flows passing a straight wedge

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