2D Navier–Stokes equation in Besov spaces of negative order Original Research Article

The Navier–Stokes equation in the bidimensional torus is considered, with initial velocity in the Besov spaces View the MathML sourceBpr−s+2−2r and forcing term in View the MathML sourceLr(0,T;Bpq−s) for suitable indices s,r,p,qs,r,p,q. Results of local existence and uniqueness are proven in the case View the MathML source−1<−s+2−2r<0 and of global existence in the case View the MathML source−12<−s+2−2r<0.