Solutions faibles globales des équations de Navier-Stokes pour un fluide compressible. (Global weak solutions for compressible Navier- Stokes equations).(French)Zbl 0597.76067

Summary: One proves the global existence for the one-dimensional Navier-Stokes equations. The fluid is compressible and either isentropic or isothermal. The initial density is of class $$BV_{loc}$$ or $$H^ s_{loc}$$, $$0<s<1$$. The total mass of the fluid is finite, but it lies on the whole real line.

MSC:

 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q30 Navier-Stokes equations