论文标题
毛细血管毛利流量引起的二维色散模型的适合度
Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows
论文作者
论文摘要
本文的目的是在几种环境中建立适当的性质，以解决与毛细血管质地研究研究中产生的模型相关的库奇问题。更确切地说，我们确定经典Sobolev空间中的局部适应性结论，以及一些适合方程能量的空间。一个关键成分是涉及希尔伯特变换和分数衍生物的换向估计。我们还研究了相关的周期性初始值问题的局部良好性。此外，通过确定各向异性加权Sobolev空间中的适当性以及一些独特的延续原则，我们表征了该模型解决方案的空间行为。作为我们结果的进一步结果，我们得出了Shrira方程的新结论，该方程出现在剪切流中的波浪中。
This paper is aimed to establish well-posedness in several settings for the Cauchy problem associated to a model arising in the study of capillary-gravity flows. More precisely, we determinate local well-posedness conclusions in classical Sobolev spaces and some spaces adapted to the energy of the equation. A key ingredient is a commutator estimate involving the Hilbert transform and fractional derivatives. We also study local well-posedness for the associated periodic initial value problem. Additionally, by determining well-posedness in anisotropic weighted Sobolev spaces as well as some unique continuation principles, we characterize the spatial behavior of solutions of this model. As a further consequence of our results, we derive new conclusions for the Shrira equation which appears in the context of waves in shear flows.
