where u = u(t, x) : R â†’ C is a complex-valued wave function, both Î» 6= 0 and k > 5 are real numbers. A great deal of interesting research has been devoted to the mathematical analysis for theâ€¦ (More)

We study the well-posedness of Cauchy problem for the fourth order nonlinear SchrÃ¶dinger equations iâˆ‚t u=âˆ’Îµ u+ 2u+ P (( âˆ‚ x u ) |Î±| 2, ( âˆ‚ x Å« ) |Î±| 2 ) , t âˆˆR, x âˆˆRn, where Îµ âˆˆ {âˆ’1,0,1}, n 2 denotesâ€¦ (More)

The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces inâ€¦ (More)

In this paper, we establish a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, the Î³-gas law equation of state for Î³ = 2 and the generalâ€¦ (More)

The GPE (1.1) in physical dimensions (2 and 3 dimensions) is used in the meanfield quantum theory of Bose-Einstein condensate (BEC) formed by ultracold bosonic coherent atomic ensembles. Recently,â€¦ (More)

We consider the Cacuhy problem for a viscous compressible rotating shallow water system with a third-order surface-tension term involved, derived recently in the modelling of motions for shallowâ€¦ (More)

Hai-Liang Li, 1 Guo-Jing Zhang, 2 Min Zhang, 1 Chengchun Hao Department of Mathematics, Capital Normal University, Beijing 100037, P.R.China Department of Mathematics, Harbin Institute of Technology,â€¦ (More)

The Cauchy problem of a multidimensional (d 2) compressible viscous liquid-gas two-phase flow model is studied in this paper. We investigate the global existence and uniqueness of the strong solutionâ€¦ (More)

In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to theâ€¦ (More)

In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid MHD equations in all physical spatial dimensions n = 2 and 3 byâ€¦ (More)