Lq‐estimates for the stationary Oseen equations on the exterior of a rotating obstacle. (30th April 2018)

• Record Type: Journal Article
• Authors: Kim, Dugyu
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 12(2018)
• Page Start: 4506
• Page End: 4527
• Publication Date: 2018-04-30
• Subjects: Lq‐estimates -- rotating obstacles -- stationary Oseen equations -- very weak solutions -- weak solutions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4911
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We study the Dirichlet problem for the stationary Oseen equations around a rotating body in an exterior domain. Our main results are the existence and uniqueness of weak and very weak solutions satisfying appropriate L q ‐estimates. The uniqueness of very weak solutions is shown by the method of cut‐off functions with an anisotropic decay. Then our existence result for very weak solutions is deduced by a duality argument from the existence and estimates of strong solutions. From this and interior regularity of very weak solutions, we finally establish the complete D 1, r ‐result for weak solutions of the Oseen equations around a rotating body in an exterior domain, where 4/3< r <4. Here, D 1, r is the homogeneous Sobolev space.