Cauchy problem for the Zakharov system arising from hot plasma with low regularity data

Global smooth solutions for the nonlinear Schrödinger equation with magnetic effect

“…Therefore, we conclude that if 0 ≤ (16C) −1 , then A T * ≤ 4 0 , which in turn implies T * = +∞. Then the decay estimates in (9) follow easily from (17) and (20). This completes the proof of Theorem 2.1.…”

“…[1,2,3,4,7,12,13,14,15,21,28,30] and the references therein. In the presence of magnetic field, we refer to [22,26] for the background of physical importance and [8,16,17,20,25,27,32] for the mathematical theories of the magnetic type Zakharov systems.…”

“…(1 + s) 1/6 A T , then by (17), (18), (20) and 11, we have (117) L 2 t e it∆ f L 6 |∇| −1 e itγ∆ (xg)…”

“…2 . On the support of 1−χ 1 , there is |η| |ξ−η|, so the N derivatives can be put on E = e is∆ f , then by (20),…”

On the limit behavior of the magnetic Zakharov system

“…For the limit behavior results of (1.1), [8] proved that the solutions of magnetic Zakharov system converged to those of generalized Zakharov system in Sobolev space H s , s > 3/2, when parameter β → ∞; when (α, β) → ∞ together, they further proved that the solutions of magnetic Zakharov system converged to those of Schrödinger equation with magnetic effect in H s , s > 3/2. For other results about magnetic Zakharov equation, we can refer to [9][10][11][12][13][14] and the references therein.…”