Existence of Global Weak Solutions for 3d Degenerate Compressible Navier-stokes Equations
نویسندگان
چکیده
In this paper, we prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation [2]. The main contribution of this paper is to derive the Mellet-Vasseur type inequality [32] for the weak solutions, even if it is not verified by the first level of approximation. This provides existence of global solutions in time, for the compressible Navier-Stokes equations, for any γ > 1 in two dimensional space and for 1 < γ < 3 in three dimensional space, with large initial data possibly vanishing on the vacuum. This solves an open problem proposed by Lions in [27].
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