Improvement of the energy method for strongly non resonant dispersive equations and applications
Improvement of the energy method for strongly non resonant dispersive equations and applications
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DOI：
10.2140/apde.2015.8.1455
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
L. Molinet;Stéphane Vento
中科院分区：
文献类型：
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作者：
L. Molinet;Stéphane Vento
在本文中，我们提出了一种新方法来证明与强非共振色散方程相关的柯西问题的局部适定性。作为一个例子，对于一大类一维色散方程，我们获得低于 $ H^1 $ 的柯西问题的无条件适定性，其色散大于或等于 Benjamin-Ono 方程的色散。由于这是在不使用规范变换的情况下完成的，这使我们能够证明这些方程的粘性版本的解对于纯色散解的强收敛结果。
In this paper we propose a new approach to prove the local well-posedness of the Cauchy problem associated with strongly non resonant dispersive equations. As an example we obtain unconditional well-posedness of the Cauchy problem below $ H^1 $ for a large class of one-dimensional dispersive equations with a dispersion that is greater or equal to the one of the Benjamin-Ono equation. Since this is done without using a gauge transform, this enables us to prove strong convergence results for solutions of viscous versions of these equations towards the purely dispersive solutions.