Inviscid limit for the energy-critical complex Ginzburg-Landau equation |
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Authors: | Chunyan Huang |
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Affiliation: | LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China |
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Abstract: | In this paper, we consider the limit behavior for the solution of the Cauchy problem of the energy-critical complex Ginzburg-Landau equation in Rn, n?3. In lower dimension case (3?n?6), we show that its solution converges to that of the energy-critical nonlinear Schrödinger equation in , T>0, s=0,1, as a by-product, we get the regularity of solutions in H3 for the nonlinear Schrödinger equation. In higher dimension case (n>6), we get the similar convergent behavior in C(0,T,L2(Rn)). In both cases we obtain the optimal convergent rate. |
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Keywords: | Complex Ginzburg-Landau equation Nonlinear Schrö dinger equation Inviscid limit Energy-critical power |
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