OSEEN SYSTEM WITH CORIOLIS TERM

Abstract

This paper is devoted to solutions of the Dirichlet problem for the Oseen system with Coriolis term –�u(z) + �� 1 u(z) – (� × z) � �u(z) + �� × u(z) + �p(z) = f (z), � . � in �, u = g on �� in the homogeneous Sobolev space 1, 3 ( ; ) ( )q q W L� � �� � with 2 � q < 3. Here �� � � 3 is an exterior domain. Kracmar, Necasová and Penel proved that if � has boundary of class � 2 , g � 0 and f � D –1,q (�; � 3 ), then there exists a unique solution of the problem. This paper shows that this result holds true even for domains with Lipschitz boundary. Moreover, we prove unique solvability of the problem for general g � W 1–1/q,q (��;� � 3 ) and f � D –1,q (�; � 3 ).