WEEKLY ACTIVITIES

Time: 9h30, Tuesday, June 9, 2015

Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: We construct mild solutions to the Navier-Stokes equations by applying the Picard contraction principle, for the Sobolev spaces $dot H^s_q$ $(q >1, frac{d}{q}-1 leq s 1, s = frac{d}{q} - 1)$ we get the existence of global mild solutions in the spaces $L^infty([0, infty); dot{H}^{frac{d}{q} - 1}_q(mathbb{R}^d))$ when the norm of the initial value is small enough. The same argument is applied to following spaces:

• Critical Sobolev-Fourier-Lorentz spaces $dot{H}^{frac{d}{p}-1}_{mathcal{L}^{p,r}} (mathbb{R}^d), (r geq 1, 1 leq p < infty)$;
• - Sobolev-Lorentz spaces $dot{H}^s_{L^{q,r}}(mathbb{R}^d), (s geq 0, q > 1, r geq 1, frac{d}{q}-1 leq s < frac{d}{q})$ with critical indexes $s =frac{d}{q}-1$.