2D Density-dependent Leray Problem with a Discontinuous Density

We consider the existence of a solution for the stationary Navier-Stokes equations describing an inhomogeneous incompressible fluid in a two dimensional unbounded Y-shaped domain. We show the existence of a weak solution such that the density and velocity of the fluid tend to densities and parallel flows, respectively, prescribed at some 'ends' of the domain. We allow prescribed densities at different ends to have distinct values. In fact, we obtain the density in the L$\infty$-space.

Keywords

stationary Navier-Stokes equations, incompressible flow, inhomogeneous fluid, Leray problem, discontinuous density

2010 Mathematics Subject Classification

35Q30, 76D05

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Published 1 January 2006