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| Compressible Limit of the Nonlinear Schr¨odinger Equation with Different-Degree Small Parameter Nonlinearities |
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Citation： |
Zaihui GAN,Boling GUO.Compressible Limit of the Nonlinear Schr¨odinger Equation with Different-Degree Small Parameter Nonlinearities[J].Chinese Annals of Mathematics B,2011,32(1):105~122 |
| Page view： 1634
Net amount： 1168 |
Authors： |
Zaihui GAN; Boling GUO; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10801102, 10771151), the
Sichuan Youth Sciences and Technology Foundation (No. 07ZQ026-009) and the China Postdoctoral Science
Foundation. |
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| Abstract： |
The authors study the compressible limit of the nonlinear Schr¨odinger equation
with different-degree small parameter nonlinearities in small time for initial data with
Sobolev regularity before the formation of singularities in the limit system. On the one
hand, the existence and uniqueness of the classical solution are proved for the dispersive
perturbation of the quasi-linear symmetric system corresponding to the initial value problem
of the above nonlinear Schr¨odinger equation. On the other hand, in the limit system,
it is shown that the density converges to the solution of the compressible Euler equation
and the validity of the WKB expansion is justified. |
Keywords： |
Nonlinear Schrodinger equation, Compressible limit, Compressible Euler
equation, WKB expansion |
Classification： |
35Q55, 35C20 |
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