ON THE CAUCHY PROBLEM FOR NONLINEAR SCHROEDINGER EQUATIONS WITH ROTATION

Paolo Antonelli; Daniel Marahrens; Christof Sparber

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ON THE CAUCHY PROBLEM FOR NONLINEAR SCHROEDINGER EQUATIONS WITH ROTATION

机译：带旋转的非线性Schedederer方程的Cauchy问题

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We consider the Cauchy problem for (energy-subcritical) nonlinear Schrodinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superfluid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable influence in proving finite time blow-up in the focusing case.

机译：我们考虑具有次二次外部势和附加角动量旋转项的（能量次临界）非线性Schrodinger方程的柯西问题。该方程是旋转陷阱中超流体量子气体的众所周知的模型。我们证明了散焦非线性的全局存在（在能量空间中），而对旋转频率没有任何限制，从而对[11，12]中给出的早期结果进行了概括。此外，我们发现旋转项在聚焦情况下证明有限时间爆炸具有相当大的影响。

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来源
《Discrete and continuous dynamical systems》 |2012年第3期|p.703-715|共13页
作者
Paolo Antonelli; Daniel Marahrens; Christof Sparber;
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作者单位

Department of Applied Mathematics and Theoretical Physics CMS, Wilberforce Road Cambridge CB3 OWA, England;

Department of Applied Mathematics and Theoretical Physics CMS, Wilberforce Road Cambridge CB3 OWA, England;

Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago 322 Science and Engineering Offices (M/C 249) 851 South Morgan Street Chicago, Illinois 60607, USA;

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正文语种 eng
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nonlinear schrodinger equation; bose-einstein condensation; rotation; angular momentum operator; finite time blow-up;

机译：非线性薛定inger方程;玻色-爱因斯坦凝聚回转;角动量算子有限时间爆炸;

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专利

1. A series solution of the Cauchy problem for the generalized d-dimensional Schroedinger equation with a power-law nonlinearity [J] . A. Shidfar, rnA. Molabahrami, rnA. Babaei, Computers & mathematics with applications . 2010,第4期

机译：具有幂律非线性的广义d维Schroedinger方程Cauchy问题的级数解
2. The Cauchy problem for non-autonomous nonlinear Schroedinger equations [J] . Peter Y. H. Pang, TANG Hongyan, WANG Youde Science in China. Series A, Mathematics, physics, astronomy . 2005,第4期

机译：非自治非线性Schroedinger方程的Cauchy问题
3. THE CAUCHY PROBLEM OF NONLINEAR SCHROEDINGER-BOUSSINESQ EQUATIONS IN H~3(R~d) [J] . Han Yongqian Journal of partial differential equations . 2005,第1期

机译：H〜3（R〜d）中非线性Schroedinger-Boussinesq方程的Cauchy问题
4. Comparison of soliton solutions of the nonlinear Schroedinger equation and the nonlinear amplitude equation [C] . A. Dakova, D. Dakova, L. Kovachev International school on quantum electronics . 2015

机译：非线性Schroedinger方程和非线性振幅方程孤子解的比较。
5. Applications of a nonlinear Ovsjannikov theorem to boundary control of nonlinear Schroedinger and Korteweg-de Vries equations. [D] . De Jager, Joel Perry. 1997

机译：非线性Ovsjannikov定理在非线性Schroedinger和Korteweg-de Vries方程的边界控制中的应用。
6. Colloquium PaperNonlinear partial differential equations and applications: On the global Cauchy problem for the nonlinear Schrödinger equation [O] . Jean Bourgain 2007

机译：非线性偏微分方程及其应用：关于非线性的整体柯西问题薛定er方程
7. The cauchy problem for the schroedinger equation in dimension three with concentrated nonlinearity [O] . Adami, Riccardo, Dell'Antonio, Gianfausto, Figari, Rodolfo, 2003

机译：具有集中非线性的三维Schroedinger方程的柯西问题
8. Vortex Nucleation in a Dissipative Variant of the Nonlinear Schroedinger Equation Under Rotation. [R] . Carretero-Gonzalez, R., Kevrekidis, P. G., Kolokolnikov, T. 2014

机译：旋转下非线性schroedinger方程耗散变量的涡核。

ON THE CAUCHY PROBLEM FOR NONLINEAR SCHROEDINGER EQUATIONS WITH ROTATION

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