论文标题
在非线性dysthe方程式上
On the nonlinear Dysthe equation
论文作者
论文摘要
这项工作致力于为二维方程式的局部良好性理论提供稳固的分析理论。该方程可以从不可压缩的Navier-Stokes方程中得出，在执行WaveTrain调制到第四阶的渐近扩展后。最近，该方程已被用来研究大型水体（例如流氓波）上的稀有现象。为了研究良好的能力，我们使用strichartz，并改善了平滑和最大功能估计。我们遵循Kenig，Ponce和Vega的开创性工作中的想法，但是由于该方程式高度各向异性，因此必须解决一些技术挑战。我们通过提出不良的结果来结束我们的工作。
This work is dedicated to putting on a solid analytic ground the theory of local well-posedness for the two dimensional Dysthe equation. This equation can be derived from the incompressible Navier-Stokes equation after performing an asymptotic expansion of a wavetrain modulation to the fourth order. Recently, this equation has been used to numerically study rare phenomena on large water bodies such as rogue waves. In order to study well-posedness, we use Strichartz, and improved smoothing and maximal function estimates. We follow ideas from the pioneering work of Kenig, Ponce and Vega, but since the equation is highly anisotropic, several technical challenges had to be resolved. We conclude our work by also presenting an ill-posedness result.
