On nonhomogeneous boundary value problem for the stationary Navier-Stokes equations in a symmetric cusp domain

Abstract

The nonhomogeneous boundary value problem for the stationary NavierStokes equations in 2D symmetric multiply connected domain with a cusp point on the boundary is studied. It is assumed that there is a source or sink in the cusp point. A symmetric solenoidal extension of the boundary value satisfying the LerayHopf inequality is constructed. Using this extension, the nonhomogeneous boundary value problem is reduced to homogeneous one and the existence of at least one weak symmetric solution is proved. No restrictions are assumed on the size of fluxes of the boundary value.

Keywords

• stationary navier–stokes equations
• nonhomogeneous boundary condition
• cusp point singularity
• multiply connected domain
• nonzero fluxes