Stationary flows for compressible viscous fluid in a perturbed half-space

Katherine Zhiyuan Zhang; Masahiro Suzuki

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arxiv 1910.05604 v2 pith:UVKIKSCW submitted 2019-10-12 math.AP math-phmath.MP

Stationary flows for compressible viscous fluid in a perturbed half-space

Masahiro Suzuki , Katherine Zhiyuan Zhang This is my paper

classification math.AP math-phmath.MP

keywords stationaryhalf-spacesolutiondirectionsperturbedcompressibleconditionplanar

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We consider the compressible Navier--Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. For a half-space, it has been known that a certain planar stationary solution exist and it is time-asymptotically stable. The planar stationary solution is independent of the tangential directions and its velocities of the tangential directions are zero. In this paper, we show the unique existence of stationary solutions for the perturbed half-space. The feature of our work is that our stationary solution depends on all directions and has multidirectional flow. Furthermore, we also prove the asymptotic stability of this stationary solution.

Stationary flows for compressible viscous fluid in a perturbed half-space

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