Local and global unique solvability of the Navier-Stokes exterior problem with Cauchy data in the space \(L^{n,\infty}\). (English) Zbl 0848.35099

Authors’ abstract: “The initial-boundary problem for the Navier-Stokes equation in exterior domains is considered for initial data in the space \(L^{n, \infty}+ L^q\) with some \(q> n\), and some sufficient conditions for the uniqueness, local solvability and global solvability are given. Even in the case \(n= 2\), some solutions with behavior different from that of Leray-Hopf solutions are treated”.
Reviewer: Th.Sonar (Hamburg)


35Q35 PDEs in connection with fluid mechanics
35Q30 Navier-Stokes equations