Steady compressible Nevier-Stokes flow in a square

Details Steady compressible Nevier-Stokes flow in a square Steady compressible Nevier-Stokes flow in a square

2009-01-26

arxiv.org/abs/0901.3996v1

Physics

Mathematical Physics

29 pages

Scientific paper

We investigate a steady flow of compressible fluid with inflow boundary condition on the density and slip boundary conditions on the velocity in a square domain in $\mathbf{R^2}$. We show existence of a strong solution $(v,\rho) \in W^2_p(Q) \times W^1_p(Q)$ that is a small perturbation of a constant flow $(\bar v \equiv [1,0],\bar \rho \equiv 1)$. We also show that this solution is unique in a class of small perturbations of the constant flow $(\bar v,\bar \rho)$. In order show the existence of the solution we adapt the techniques know from the theory of weak solutions. We apply the method of elliptic regularization and a fixed point argument.

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