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We study the well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations i∂t u=−ε u+ 2u+ P (( ∂ x u ) |α| 2, ( ∂ x ū ) |α| 2 ) , t ∈R, x ∈Rn, where ε ∈ {−1,0,1}, n 2 denotes the spatial dimension and P(·) is a polynomial excluding constant and linear terms. © 2006 Elsevier Inc. All rights reserved.

- L. Hsiao
- 2007

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, several research groups [9, 12–14] have produced quantized vortices in trapped BECs, and a typical method they used is to impose a laser beam on the magnetic trap… (More)

- Ronghua Pan, Ling Hsiao
- 2005

It is conjectured that Darcy’s law governs the motion of compressible porous media flow in large time. This has been justified for one-dimensional isentropic flows. In this work, we show the conjecture is true for one-dimensional adiabatic flows with generic small smooth initial data. © 2004 Elsevier Inc. All rights reserved.

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 shallow water with free surface in a rotating sub-domain [18]. The global existence of the solution in the space of Besov type is shown for initial data close to a constant… (More)

- HONGJUN YU, LING HSIAO
- 2007

Global classical solutions near Maxwellians are constructed for the Boltzmann and Landau equations with soft potentials in the whole space. The construction of global solutions is based on refined energy analysis. Our results generalize the classical results in Ukai and Asano (Publ. Res. Inst. Math. Sci. 18 (1982), 477–519) to the very soft potentials for… (More)

- Ling Hsiao, Norbert J. Mauser, Kai-Jun Mang
- Appl. Math. Lett.
- 2004

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 R .

- FRANCISCO GUILLÉN GONZÁLEZ, MÁRCIO SANTOS, DA ROCHA, ANDMARKO ROJAS MEDAR, Ling Hsião
- 2005

where the unknown are u, θ, π which denote, respectively, the velocity field, the scalar temperature and the scalar pressure. Data are the positive constants ν, χ, respectively, the viscosity and the thermal conductivity coefficients and the function f the external force field, and a(x), b(x), respectively, represent the initial velocity and initial… (More)

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