2022-05-25T11:14:49Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698962018-04-25T23:44:12Zhdl_2115_45007hdl_2115_116The Navier-Stokes equations with initial values in Besov spaces of type $B_{q,\infty}^{-1+3/q}$Farwig, ReinhardGIGA, YOSHIKAZUHsu, Pen-YuanInstationary Navier-Stokes systeminitial valueslocal strong solutionsweighted Serrin conditionlimiting type of Besov spacerestricted Serrin's uniqueness theorem410We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain R3 with initial value u0 2 L2 ( ). It is known that a weak solution is a local strong solution in the sense of Serrin if u0 satis es the optimal initial value condition u0 2 B1+3=q q;sq with Serrin exponents sq > 2; q > 3 such that 2 sq + 3 q = 1. This result has recently been generalized by the authors to Rweighted Serrin conditions such that u is contained in the weighted Serrin class T 0 ( ku( )kq)s d < 1 with 2 s + 3 q = 1 2 , 0 < < 1 2 . This regularity is guaranteed if and only if u0 is contained in the Besov space B1+3=q q;s . In this article we consider the limit case of initial values in the Besov space B1+3=q q;1 and in its subspace B 1+3=q q;1 based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69896info:doi/10.14943/84236https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69896/1/pre1092.pdfHokkaido University Preprint Series in Mathematics10921212016-06-20engpublisher