On the Initial Value Problem for the Navier-Stokes Equations with the Initial Datum in Critical Sobolev and Besov Spaces

Journal of Mathematical Sciences

Khai, D. Q.¹  Tri, N. M.¹ 

关键词: Navier-Stokes equations;    existence and uniqueness of local and global mild solutions;    critical Sobolev and Besov spaces.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

TheexistenceoflocaluniquemildsolutionstotheNavier-StokesequationsinthewholespacewithaninitialtempereddistributiondatumincriticalhomogeneousorinhomogeneousSobolevspacesisshown.Especially,thecasewhentheintegral-exponentislessthan2isinvestigated.TheglobalexistenceisalsoobtainedfortheinitialdatumincriticalhomogeneousSobolevspaceswithanormsmallenoughinsuitablecriticalBesovspaces.Thekeylemmaistoestablishthebilinearestimatesinthesespaces,duetothepoint-wisedecayofthekerneloftheheatsemigroup.

【 授权许可】

Unknown