000219463 001__ 219463
000219463 005__ 20181203024249.0
000219463 0247_ $$2doi$$a10.1007/s00574-016-0135-0
000219463 022__ $$a1678-7544
000219463 02470 $$2ISI$$a000372554400018
000219463 037__ $$aARTICLE
000219463 245__ $$aAn overview of some recent results on the Euler system of isentropic gas dynamics
000219463 260__ $$aHeidelberg$$bSpringer Heidelberg$$c2016
000219463 269__ $$a2016
000219463 300__ $$a13
000219463 336__ $$aJournal Articles
000219463 520__ $$aThis overview is concerned with the well-posedness problem for the isentropic compressible Euler equations of gas dynamics. The results we present are in line with the programof investigatingthe efficiency of different selection criteria proposed in the literature in order to weed out non-physical solutions to more-dimensional systems of conservation laws and they build upon the method of convex integration developed by De Lellis and Sz,kelyhidi for the incompressible Euler equations. Mainly following [5], we investigate the role of the maximal dissipation criterion proposed by Dafermos in [6]: we prove how, for specific pressure laws, some non-standard (i.e. constructed via convex integration methods) solutions to the Riemann problem for the isentropic Euler system in two space dimensions have greater energy dissipation rate than the classical self-similar solution emanating from the same Riemann data. We therefore show that the maximal dissipation criterion proposed by Dafermos does not favour in general the self-similar solutions.
000219463 6531_ $$ahyperbolic systems of conservation laws
000219463 6531_ $$aRiemann problem
000219463 6531_ $$aadmissible solutions
000219463 6531_ $$aentropy rate criterion
000219463 6531_ $$aill-posedness
000219463 6531_ $$aconvex integration
000219463 700__ $$0247580$$aChiodaroli, Elisabetta$$g240935$$uEcole Polytech Fed Lausanne, Stn 8, CH-1015 Lausanne, Switzerland
000219463 700__ $$aKreml, Ondrej
000219463 773__ $$j47$$k1$$q241-253$$tBulletin Of The Brazilian Mathematical Society
000219463 909C0 $$0252322$$pPDE$$xU12235
000219463 909CO $$ooai:infoscience.tind.io:219463$$pSB$$particle
000219463 917Z8 $$x178574
000219463 937__ $$aEPFL-ARTICLE-219463
000219463 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000219463 980__ $$aARTICLE