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

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

2008-09-11

arxiv.org/abs/0809.1903v4

Mathematics

Analysis of PDEs

19 pages

Scientific paper

Considering the Cauchy problem for the modified Korteweg-de Vries-Burgers equation $u_t+u_{xxx}+\epsilon |\partial_x|^{2\alpha}u=2(u^{3})_x, u(0)=\phi$, where $0<\epsilon,\alpha\leq 1$ and $u$ is a real-valued function, we show that it is uniformly globally well-posed in $H^s (s\geq1)$ for all $\epsilon \in (0,1]$. Moreover, we prove that for any $s\geq 1$ and $T>0$, its solution converges in $C([0,T]; H^s)$ to that of the MKdV equation if $\epsilon$ tends to 0.

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