Time: 9h, Wednesday, May 20, 2020
Location: Room 511, Building A6, Institute of Mathematics

Abstract: Cannone and Planchon (1999) presented two different existence and uniqueness algorithms for constructing global mild solutions to the Cauchy problem for the Navier-Stokes equations with the initial data in L^3(R^3). The first algorithm and the second algorithm base on the frame of the homogeneous Besov space and homogeneous Triebel space, respectively. In this talk, we generalize the second algorithm. More precisely, we study local well-posedness for the Navier-Stokes equations with arbitrary initial data in homogeneous Sobolev spaces H^s_p(R^d) for d >= 2, p > d/2 , and d/p - 1 <= s d/2p. In the case of critical indexes s = d/p-1, we prove global well-posedness for Navier-Stokes equations when the norm of the initial value is small enough in a suitable Triebel space.