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- Title
On cauchy problem of the Benney-Lin equation with low regularity initial data.
- Authors
Xiang Qing Zhao; Shang Bin Cui
- 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.
- Subjects
CAUCHY problem; PARTIAL differential equations; BOUNDARY value problems; NUMERICAL analysis; MATHEMATICAL analysis
- Publication
Acta Mathematica Sinica, 2009, Vol 25, Issue 12, p2157
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-009-7029-7