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Title: Compressible Navier–Stokes equations with heterogeneous pressure laws
Abstract This paper concerns the existence of global weak solutions à la Leray for compressible Navier–Stokes equations with a pressure law which depends on the density and on time and space variables t and x . The assumptions on the pressure contain only locally Lipschitz assumption with respect to the density variable and some hypothesis with respect to the extra time and space variables. It may be seen as a first step to consider heat-conducting Navier–Stokes equations with physical laws such as the truncated virial assumption. The paper focuses on the construction of approximate solutions through a new regularized and fixed point procedure and on the weak stability process taking advantage of the new method introduced by the two first authors with a careful study of an appropriate regularized quantity linked to the pressure.  more » « less
Award ID(s):
2049020
PAR ID:
10341400
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Nonlinearity
Volume:
34
Issue:
6
ISSN:
0951-7715
Page Range / eLocation ID:
4115 to 4162
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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