Sharp well-posedness and ill-posedness of the Navier-Stokes initial value problem in Besov-type spaces

2015/05/05 by Cui, Shangbin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.00865

Abstract

We prove that the Navier-Stokes initial value problem is well-posed in the logrithmically refined Besov spaces when the second index is not less than certain critical value, and ill-posed in such spaces when the second index is less than this critical value. The well-posedness result is proved by using some sharp bilinear estimates obtained from some Hardy-Littlewood type inequalities. The ill-posedness assertion is proved by refining the arguments of Wang [18] and Yoneda [20].

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