Global well posedness and inviscid limit for the Korteweg-de Vries-Burgers equation

Abstract

Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation \begin{eqnarray*} u_t+u_{xxx}+ε|\partial_x|^{2α}u+(u^2)_x=0, \ u(0)=ϕ, \end{eqnarray*} where $0<\epsilon ,\alpha \le 1$ and $u$ is a real-valued function, we show that it is globally well-posed in $H^s(s>s_{\alpha })$, and uniformly globally well-posed in $H^s(s>-3/4)$ for all $\epsilon \in (0,1)$. Moreover, we prove that for any $T>0$, its solution converges in $C([0,T];H^s)$ to that of the KdV equation if $\epsilon$ tends to 0.

arXiv comment35 pages, 0 figure

References in corpus (1)

• Global well-posedness for dissipative Korteweg-de Vries equations

Cited by in corpus (2)

• Global Well-posedness of Korteweg-de Vries equation in $H^{-3/4}(\mathbb{R})$
• Global well-posedness and inviscid limit for the modified Korteweg-de Vries-Burgers equation