Existence and Regularity of Very Weak Solutions of the Stationary Navier-Stokes Equations

초록

We consider the stationary Navier-Stokes equations in a bounded domain Omega in R(n) with smooth connected boundary, where n = 2, 3 or 4. In case that n = 3 or 4, existence of very weak solutions in L(n)(Omega) is proved for the data belonging to some Sobolev spaces of negative order. Moreoverwe obtain complete L(q)-regularity results on very weak solutions in L(n)(Omega). If n = 2, then similar results are also proved for very weak solutions in L(q0)(Omega) with any q(0) > 2. We impose neither smallness conditions on the external force nor boundary data for our existence and regularity results.

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