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SUMMARY In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an rotational angular momentum term in the space R 2 .

We study the wellposedness of Cauchy problem for the fourth order nonlinear Schrödinger equations i∂ t u = −ε∆u + ∆ 2 u + P (∂ α x u) |α|2 , (∂ α x ¯ u) |α|2 , t ∈ R, x ∈ R n , where ε ∈ {−1, 0, 1}, n 2 denotes the spatial dimension and P (·) is a polynomial excluding constant and linear terms.

- Ling Hsiao, Ronghua Pan
- 1999

We study a rate-type viscoelastic system proposed by I. which is a 3_3 hyperbolic system with relaxation. As the relaxation time tends to zero, this system convergences to the well-known p-system formally. In the case where the initial data are the Riemann data such that the corresponding solutions of the p-system are centered rarefaction waves, we show… (More)

- Ling Hsiao, Ronghua Pan
- 1999

We study the initial value problem for the system of compressible adiabatic flow through porous media in the one space dimension with fixed boundary condition. Under the restriction on the oscillations in the initial data, we establish the global existence and large time behavior for the classical solutions via the combination of characteristic analysis and… (More)

- L. Hsiao
- 2007

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… (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.

- 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 3 .