Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations
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In this article, the authors study the Riemann problem for multidimensional compressible isentropic Euler equations using the framework developed in Chiodaroli et al. using the techniques of De Lellis and Szekelyhidi.Abstract:
We study the Riemann problem for multidimensional compressible isentropic Euler equations Using the framework developed in Chiodaroli et al (2015 Commun Pure Appl Math 68 1157–90), and based on the techniques of De Lellis and Szekelyhidi (2010 Arch Ration Mech Anal 195 225–60), we extend the results of Chiodaroli and Kreml (2014 Arch Ration Mech Anal 214 1019–49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutionsread more
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The Riemann Problem for the Multidimensional Isentropic System of Gas Dynamics is Ill-Posed if It Contains a Shock
TL;DR: In this article, the authors considered the isentropic compressible Euler equations in two space dimensions together with particular initial data and showed that the solution is non-unique in all cases.
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The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock
TL;DR: In this article, the authors considered the isentropic compressible Euler equations in two space dimensions together with particular initial data and showed that the solution is non-unique in all cases.
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Stability of Planar Rarefaction Wave to Two-Dimensional Compressible Navier--Stokes Equations
Lin-an Li,Yi Wang +1 more
TL;DR: It is proved that the time-asymptotically nonlinear stability of the planar rarefaction wave to the two-dimensional compressible and isentropic Navier-Stokes equations is given, which gives the first stability result of the Planar Rarefaction Wave to the multi-dimensional system with physical viscosities.
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Kolmogorov-type theory of compressible turbulence and inviscid limit of the Navier–Stokes equations in R3
Gui-Qiang Chen,James Glimm +1 more
TL;DR: In this article, the inviscid limit of the Navier-Stokes equations to the Euler equations for compressible fluids in R 3 was studied and a Kolmogorov-type hypothesis for barotropic flows was introduced, in which the density and the sonic speed normally vary significantly.
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Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations
Lin-an Li,Teng Wang,Yi Wang +2 more
TL;DR: In this article, the authors prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain.
References
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Hyperbolic Conservation Laws
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On admissibility criteria for weak solutions of the Euler equations
TL;DR: In this article, the authors consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities, and show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution.
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