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| Sharp Threshold of Global Existence for a Nonlocal Nonlinear Schr\"{o}dinger System in R3 |
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Citation： |
Zaihui GAN,Xin JIANG,Jing LI.Sharp Threshold of Global Existence for a Nonlocal Nonlinear Schr\"{o}dinger System in R3[J].Chinese Annals of Mathematics B,2019,40(1):131~160 |
| Page view： 1398
Net amount： 948 |
Authors： |
Zaihui GAN; Xin JIANG;Jing LI |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11571254). |
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| Abstract： |
In this paper, the authors investigate the sharp threshold of a
three-dimensional nonlocal nonlinear Schr\"{o}dinger system. It is a
coupled system which provides the mathematical modeling of the
spontaneous generation of a magnetic field in a cold plasma under
the subsonic limit. The main difficulty of the proof lies in
exploring the inner structure of the system due to the fact that the
nonlocal effect may bring some hinderance for establishing the
conservation quantities of the mass and of the energy, constructing
the corresponding variational structure, and deriving the key
estimates to gain the expected result. To overcome this, the authors
must establish local well-posedness theory, and set up suitable
variational structure depending crucially on the inner structure of
the system under study, which leads to define proper functionals and
a constrained variational problem. By building up two invariant
manifolds and then making a priori estimates for these nonlocal
terms, the authors figure out a sharp threshold of global existence
for the system under consideration. |
Keywords： |
Nonlocal nonlinear Schr"{o}dinger system,Sharp threshold, Blow-up, Global existence |
Classification： |
35A15, 35E55, 35Q55 |
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