Very weak solutions of the stationary Navier-Stokes equations for an incompressible fluid past obstacles

초록

We consider the stationary motion of an incompressible Navier-Stokes fluid past obstacles in R-3, subject to the given boundary velocity v(b), external force f = div F and nonzero constant vector ke(1) at infinity. Our main result is the existence of at least one very weak solution v in ke(1) + L-3(Omega) for arbitrary large F is an element of L-3/2(Omega)+ L-12/7(Omega) provided that the flux of vb-ke(1) on the boundary of each body is sufficiently small with respect to the viscosity.. The uniqueness of very weak solutions is proved by assuming that F and v(b)-ke(1) are suitably small. Moreover, we establish weak and strong regularity results for very weak solutions. In particular, our existence and regularity results enable us to prove the existence of a weak solution v satisfying del v is an element of L-3/2(Omega). (C) 2016 Elsevier Ltd. All rights reserved.

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