Lions, Pierre-Louis Global existence of solutions for isentropic compressible Navier-Stokes equations. (Existence globale de solutions pour les équations de Navier-Stokes compressibles isentropiques.) (French. Abridged English version) Zbl 0778.76086 C. R. Acad. Sci., Paris, Sér. I 316, No. 12, 1335-1340 (1993). Summary: We present global existence results for weak solutions of isentropic, compressible Navier-Stokes equations in arbitrary dimensions \((N\geq 2)\) with arbitrary initial data (finite mass and total energy). In the case of a pressure law \(p(\rho)=a\rho^{\gamma}(a>0)\), the result is shown under the condition \(\gamma\geq \gamma_ 0(N)\) with \(\gamma_ 0(2)=3/2\) for example. The proof relies upon “stability” properties of sequences of solutions and on appropriate approximations based upon, for instance, the study of stationary problems. And we give, for these stationary problems, existence results of weak solutions and regularity results if \(N=2\) or if \(N=3\). Cited in 1 ReviewCited in 30 Documents MSC: 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q30 Navier-Stokes equations Keywords:stability properties; weak solutions; stationary problems; regularity PDFBibTeX XMLCite \textit{P.-L. Lions}, C. R. Acad. Sci., Paris, Sér. I 316, No. 12, 1335--1340 (1993; Zbl 0778.76086)