Physically reasonable solutions to steady compressible Navier-Stokes equations in 3D exterior domains \((v_ \infty\neq 0)\)
We consider steady compressible Navier-Stokes equations in barotropic, isentropic or isothermal regime in three-dimensional exterior domains with the velocity at infinity equal to a strictly nonzero constant vector. Under the assumptions on the smallness of the external force and of the prescribed velocity at infinity, we prove existence and uniqueness of solutions, in the class of functions possessing the same pointwise decay as the fundamental Oseen tensor. In particular, we prove existence of the wake region, where the velocity and its gradients decay more slowly then outside it; the decay rate corresponds to that one of the Oseen equation. In this sense, the result is optimal. Further, the (singular) limit when the velocity at infinity tends to zero, is investigated. The main tool in the proof is the method of decomposition.
scientific article; zbMATH DE number 1057248