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].
Reference
- 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.
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