Weak solutions for the Navier-Stokes equations with B-infinity infinity(-1(ln)) B-Xr(-1 r,2/1-r) L-2 initial data

作者：Cui; Shangbin

来源：Journal of Mathematical Physics, 2013, 54(5): 051503.

DOI：10.1063/1.4798790

One of the major topics in the study of nonlinear partial differential equations of the evolutionary type is to look for as large as possible initial value spaces so that as many as possible solutions of such equations can be obtained. In the book "Recent Developments in the Navier-Stokes Problems," Lemarie-Rieusset proved that the Navier-Stokes equations have global weak solutions for initial data in the space B-(X) over tilder(-1 r,2/1-r)(R-N) L-2(R-N) (0 < r < 1), where X-r is the space of functions whose pointwise products with H-r functions belong to L-2, (X) over tilde (r) denotes the closure of C-0(infinity)(R-N) in X-r, and B-(X) over tilder(-1 r,2/1-r)(R-N) is the Besov space over (X) over tilde (r). In this paper we partially extend this result of Lemarie-Rieusset to the larger initial value space B-infinity infinity(-1(ln))(R-N) B-(X) over tilder(-1 r,2/1-r)(R-N) L-2(R-N) (0 < r < 1), where B-infinity infinity(-1(ln))(R-N) is a logarithmically modified version of the usual Besov space B-infinity infinity(-1)(R-N).

• 出版日期2013-5
• 单位中山大学