Thu, 03 Dec 2015
12:00 -
13:00
L6
Weak solutions to the Navier-Stokes initial boundary value problem in exterior domains with initial data in L(3,∞)
Paolo Maremonti
(Seconda Università degli Studi di Napoli)
Abstract
We consider the Navier-Stokes initial boundary value problem (NS-IBVP) in a smooth exterior domain. We are interested in establishing existence of weak solutions (we mean weak solutions as synonym of solutions global in time) with an initial data in L(3,∞)
(Lorentz space). Apart from its own analytical interest, the research is connected with questions related to the space-time asymptotic properties of solutions to the NS-IBVP. However these questions are not discussed. The assumption on the initial data in L(3,∞) cuts the L2-theory out, which is the unique known for weak solutions. We find a simple strategy to bypass the difficulties of an initial data /∈ L2, and we take care to perform the same “regularity properties” of Leary’s weak solutions, hence to furnish a structure theorem of a weak solution.