实线上耗散KdV方程的Sharp适定性和病态性结果
IF 0.7
Q3 MATHEMATICS, APPLIED
引用次数: 12
摘要
本文研究了以下广义KdV- Burgers方程的柯西问题 % \begin{equation*} \left\{\begin{array}{l} \partial_tu+\partial_x^3u+L_pu+u\partial_xu=0, u(0,\,x)=u_0(x). \end{array} \right. \end{equation*} % where $L_p$ is a dissipative multiplicator operator. Using Besov-Bourgain Spaces, we establish a bilinear estimate and following the framework developed in Molinet, L. & Vento, S. (2011) we prove sharp global well-posedness in the Sobolev spaces $H^{-p/2}(I\!\!R)$ and sharp ill-posedness in $H^s(I\!\!R)$ when $s<-p/2$ with $p \geq 2$.本文章由计算机程序翻译，如有差异，请以英文原文为准。
Sharp well-posedness and ill-posedness results for dissipative KdV equations on the real line
This work is concerned about the Cauchy problem for the following generalized KdV- Burgers equation
%
\begin{equation*}
\left\{\begin{array}{l}
\partial_tu+\partial_x^3u+L_pu+u\partial_xu=0,
u(0,\,x)=u_0(x).
\end{array}
\right.
\end{equation*}
%
where $L_p$ is a dissipative multiplicator operator. Using Besov-Bourgain Spaces, we establish a bilinear estimate and following the framework developed in Molinet, L. & Vento, S. (2011) we prove sharp global well-posedness in the Sobolev spaces $H^{-p/2}(I\!\!R)$ and sharp ill-posedness in $H^s(I\!\!R)$ when $s<-p/2$ with $p \geq 2$.
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