Global strong solutions to the incompressible Navier-Stokes equations with density-dependent viscosity
The 3D incompressible Navier-Stokes equations are studied, when the fluid viscosity is depending on the density, in a smooth domain. When the mass of fluid or the density are small enough, the authors obtain the well-posedness of the strong solutions. When the vacuum is allowed, the compatibility condition (1.4), introduced in [\textit{Y. Cho} and \textit{H. Kim}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 59, No. 4, 465--489 (2004; Zbl 1066.35070)] is used. The norm of the viscosity gradient in a Sobolev space \(L^q\) is considered bounded. This hypothesis allows the use of some regularity results for Stokes equations.
scientific article; zbMATH DE number 6607794
scientific article