Global weak solutions to the 1D compressible Euler equations with radiation

variant of a result of De Lellis and Székelyhidi [11] (cf. Remark 3.2 below) and show the existence of infinitely many global-in-time 3 weak solutions to the problem (1.1)–(1.6) for

The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method

(2010) [2] we show that, in the case of periodic boundary conditions and for arbitrary space dimension d 2, there exist infinitely many global weak solutions to the

in Sobolev spaces of sufficiently high order, then we show the existence of a solution in a particular case and finally we solve the general case by using the

The motivation of this study derives mostly from the problem of the convergence of the so called Smoothed Particle Hydrodynamics (SPH) method, a numerical scheme

Algorithm 2.. It is possible to simplify it. By using the Euler equations in the subdomain, we have lowered the degree of the derivatives in the boundary conditions. After

We finally obtain a class of schemes which offer many interesting properties: both the density and internal energy positivity are preserved, unconditionnally for the pressure

BEIRÃO DA VEIGA, The stability of one dimensional stationary flows of compressible viscous fluids, Quaderni dell’Istituto di Matematiche Appli-. cate