On the regularization of the pressure field in compressible Euler equations. (English) Zbl 0891.35123
The aim of the present paper is to state the convergence, in Sobolev norm, of the solutions of a regularized version of the Euler equations for compressible flow to the corresponding solutions of the genuine system of Euler equations for a generic polytropic fluid.
Reviewer: V.A.Sava (Iaşi)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q05 | Euler-Poisson-Darboux equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
Keywords:
regularized Euler equations; Sobolev norms; mollifiers; regularization of the pressure fieldReferences:
| [1] | S. Caprino - R. Esposito - R. Marra - M. Pulvirenti , ” Hydrodynamic limits of the Vlasov equation ” , Comm. Partial Differential Equations 18 ( 1993 ), 805 - 820 . Zbl 0787.35070 · Zbl 0787.35070 · doi:10.1080/03605309308820951 |
| [2] | R. Di Lisio - E. Grenier - M. Pulvirenti , On the convergence of the SPH method, in Special issue devoted to Simulations Methods in Kinetic Theory , C. Cercignani and R. Illner (eds.), Computers and Mathematics with Applications , 1995 . Zbl 0906.76065 · Zbl 0906.76065 · doi:10.1016/S0898-1221(97)00260-5 |
| [3] | A. Majda , Compressible Fluid Flow and System of Conservations Laws in Several Space Variables , Springer-Verlag , New York , 1984 . Zbl 0537.76001 · Zbl 0537.76001 |
| [4] | K. Oelschläger , On the connection between Hamiltonian many-particle systems and hydrodynamical equations , Arch. Rat. Mech. Anal . 115 ( 1991 ), 297 - 310 . Zbl 0850.70166 · Zbl 0850.70166 · doi:10.1007/BF00375277 |
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