Do you want to publish a course? Click here

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

161   0   0.0 ( 0 )
 Added by Chengchun Hao Dr.
 Publication date 2008
  fields
and research's language is English




Ask ChatGPT about the research

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 $Real^3$.



rate research

Read More

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 $Real^2$.
In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar auxiliary variable approach which is proposed in the recent papers [J. Comput. Phys., 416 (2018) 353-407 and SIAM Rev., 61(2019) 474-506] for developing energy stable schemes for gradient flow systems, we firstly reformulate the Gross-Pitaevskii equation into an equivalent system with a modified energy conservation law. The reformulated system is then discretized by the Gauss collocation method in time and the standard Fourier pseudo-spectral method in space, respectively. We show that the proposed schemes can preserve the discrete mass and modified energy exactly. Numerical results are addressed to verify the efficiency and high-order accuracy of the proposed schemes.
The initial value problem for the $L^{2}$ critical semilinear Schrodinger equation in $R^n, n geq 3$ is considered. We show that the problem is globally well posed in $H^{s}({Bbb R^{n}})$ when $1>s>frac{sqrt{7}-1}{3}$ for $n=3$, and when $1>s> frac{-(n-2)+sqrt{(n-2)^2+8(n-2)}}{4}$ for $n geq 4$. We use the ``$I$-method combined with a local in time Morawetz estimate.
71 - Elena Kopylova 2019
We prove global well-posedness for 3D Dirac equation with a concentrated nonlinearity.
We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by Gerard cite{Gerard}. In this paper we prove scattering for small data in the same space with some additional angular regularity, and in particular in the radial case we obtain small energy scattering.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا