ARMA manuscript No. (will be inserted by the editor) On infinite energy solutions to the Navier–Stokes equations: global 2D existence and 3D weak-strong uniqueness ISABELLE GALLAGHER, FABRICE PLANCHON Abstract This paper studies the bidimensional Navier–Stokes equations with large ini- tial data in the homogeneous Besov space _B 2 r 1 r;q (R 2 ). As long as r; q < +1, global existence and uniqueness of solutions are proved. We also prove that weak– strong uniqueness holds for the d-dimensional equations with data in _B d r 1 r;q (R d )\ L 2 (R d ) for d=r + 2=q 1. 1. Introduction We are interested in solving the 2D incompressible Navier-Stokes system in the whole space, say 8 > < > : @u @t = u u rurp; r u = 0; u(x; 0) = u 0 (x); x 2 R 2 ; t 0: (1.1) The vector field u(t; x) stands for the velocity of the fluid, the scalar field p for its pressure, and r u = 0 means that the fluid is incompressible.
- vector field
- leray solutions
- global existence
- navier stokes equations
- only known
- interpolation between
- besov space
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