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On Cauchy Problem of the Benney-Lin Equation with Low Regularity Initial Data

On Cauchy Problem of the Benney-Lin Equation with Low Regularity Initial Data
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摘要 In this work we prove that the initial value problem of the Benney-Lin equation ut + uxxx + β(uxx + u xxxx) + ηuxxxxx + uux = 0 (x ∈ R, t ≥0 0), where β 〉 0 and η∈R, is locally well-posed in Sobolev spaces HS(R) for s ≥ -7/5. The method we use to prove this result is the bilinear estimate method initiated by Bourgain. In this work we prove that the initial value problem of the Benney-Lin equation ut + uxxx + β(uxx + u xxxx) + ηuxxxxx + uux = 0 (x ∈ R, t ≥0 0), where β 〉 0 and η∈R, is locally well-posed in Sobolev spaces HS(R) for s ≥ -7/5. The method we use to prove this result is the bilinear estimate method initiated by Bourgain.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第12期2157-2168,共12页 数学学报(英文版)
基金 supported by National Natural Science Foundation of China (Grant No.10771223)
关键词 Benney-Lin equation initial value problem local well-posedness Benney-Lin equation, initial value problem, local well-posedness
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