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Abstract We study the local smoothing effects and wellposedness of Cauchy problem for the fourth order nonlinear Schrodinger equations in 1D i ∂ t u = ∂ x 4 u + P ( ( ∂ x α u ) | α | ⩽ 2 , ( ∂ x α u… (More)

- Chengchun Hao, Tao Luo
- 2014

In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid magnetohydrodynamics equations in all physical spatial dimensions n =… (More)

- Chengchun Hao
- 2011

This paper is concerned with the Cauchy problem of the compressible viscous magnetohydrodynamic (MHD) system in whole spatial space Rd for d⩾3. It is shown that the global solution exists uniquely in… (More)

- Chengchun Hao
- 2017

For the free boundary problem of the plasma–vacuum interface to 3D ideal incompressible magnetohydrodynamics, the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a… (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 the… (More)

Abstract We study the well-posedness of Cauchy problem for the fourth order nonlinear Schrodinger equations i ∂ t u = − e Δ u + Δ 2 u + P ( ( ∂ x α u ) | α | ⩽ 2 , ( ∂ x α u ¯ ) | α | ⩽ 2 ) , t ∈ R ,… (More)

- Chengchun Hao
- 2012

We investigate the Cauchy problem of a multidimensional chemotaxis model with initial data in critical Besov spaces. The global existence and uniqueness of the strong solution is shown for initial… (More)

- Chengchun Hao
- 2007

In this paper, we investigate the one-dimensional derivative nonlinear Schr\"odinger equations of the form $iu_t-u_{xx}+i\lambda\abs{u}^k u_x=0$ with non-zero $\lambda\in \Real$ and any real number… (More)

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 © 2007 John Wiley &… (More)

- Chengchun Hao, Dehua Wang
- 2016

A free boundary problem for the incompressible neo-Hookean elastodynamics is studied in two and three spatial dimensions. The a priori estimates in Sobolev norms of solutions with the physical vacuum… (More)