Hai-ang Li

Global existence for compressible Navier–Stokes–Poisson equations in three and higher dimensions

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 in three and higher dimensions.

Well-posedness for a multidimensional viscous liquid-gas two-phase flow model

The Cauchy problem of a multi-dimensional (

Global well posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions

d\geqslant 2

Global well posedness for the Gross-Pitaevskii equation with an angular momentum rotational term

) compressible viscous liquid-gas two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness of the strong solution for the initial data close to a stable equilibrium and the local in time existence and uniqueness of the solution with general initial data in the framework of Besov spaces. A continuation criterion is also obtained for the local solution.

Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors

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 the isotropic trapping frequency in the space R3.

Long-time self-similar asymptotic of the macroscopic quantum models

In this paper, we establish the global well posedness of the Cauchy problem for the Gross–Pitaevskii equation with a rotational angular momentum term in the space ℝ2. Copyright

MODIFIED SCATTERING FOR BIPOLAR NONLINEAR SCHRODINGER-POISSON EQUATIONS

Abstract The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in R 3 . We prove that the unique strong solution exists and converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and that of the classical drift–diffusion system under the combined relaxation and semiclassical limits.

Optimal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system in R^3

The unipolar and bipolar macroscopic quantum models derived recently, for instance, in the area of charge transport are considered in spatial one-dimensional whole space in the present paper. These models consist of nonlinear fourth-order parabolic equation for unipolar case or coupled nonlinear fourth-order parabolic system for bipolar case. We show for the first time the self-similarity property of the macroscopic quantum models in large time. Namely, we show that there exists a unique global strong solution with strictly positive density to the initial value problem of the macroscopic quantum models which tends to a self-similar wave (which is not the exact solution of the models) in large time at an algebraic time-decay rate.

The quasineutral limit of compressible Navier–Stokes–Poisson system with heat conductivity and general initial data

In this paper, we study the asymptotic behavior in time and the existence of the modified scattering operator of the globally defined smooth solutions to the Cauchy problem for the bipolar nonlinear Schrodinger–Poisson equations with small data in the space ℝ3.