Well-posedness for the Navier-Stokes equations with datum in the mixed-norm Sobolev-Lorentz spaces
Speaker: Dao Quang Khai

Time: 9h30, Tuesday, February 3, 2015

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

Abstract::   For 0 \leq  m< infty and index ectors q =(q_1, q_2, ..., q_d), r =(r_1, r_2, ..., r_d), where 1 \leq q_i<\infy, l =  r_i =infty, and 1 \leq   i  \leq  d we ntroduce  and  stdy  mixed-norm Sobolev-Loretz spaces dot{H}^m_{L^{ q, r}}, which are  more general than the classical Sobolev spaces dot{H}^s_q.  Then we investigate the existence and uniqueness of solutions to the Navier-Stokes equations (NSE) in the spaces  L^p([0, T]; dot{H}^m_{L^{q,r}}),  where m, q,r may take some suitable values. In the case when m = 0, q_1 = q_2 = .  . . = q_d = r_1 = r_2 = . . . =  r_3, our results recover the those the Faber, Jones and Riviere [1].


  1. E. Fabes, B. Jones N. Riviere, The initial value problem for the Navier-Stokes equations with data in L^p, Arch. Rat. Mech. Anal. 45 (1972), pp. 222-240.