On cauchy problem of the Benney-Lin equation with low regularity initial data |
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| Authors: | Xiang Qing Zhao Shang Bin Cui |
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| Institution: | [1]Department of Mathematics, Zhejiang Ocean University, Zhoushan 316000, P. R. China [2]Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China [3]Institute of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China |
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| Abstract: | In this work we prove that the initial value problem of the Benney-Lin equation u
t
+ u
xxx
+ β(u
xx + u
xxxx
) + ηu
xxxxx
+ uu
x
= 0 (x ∈ ℝ, t ≥ 0), where β > 0 and η ∈ ℝ, is locally well-posed in Sobolev spaces H
s
(R) for s ≥ −7/5. The method we use to prove this result is the bilinear estimate method initiated by Bourgain. |
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| Keywords: | Benney-Lin equation initial value problem local well-posedness |
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