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

By Zihua Guo, Baoxiang Wang. 2008

46 citations recorded by the source corpus.

Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation \begin{eqnarray*} u_t+u_{xxx}+\epsilon |\partial_x|^{2\alpha}u+(u^2)_x=0, \ u(0)=\phi, \end{eqnarray*} where $0 s_\alpha)$, 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b0b5074f04c4fab7c516399b309559f717f3612b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Zihua Guo
2. Didier Pilod
3. Carlos E. Kenig

In Mathematical Physics

1. Zihua Guo
2. Carlos E. Kenig
3. Didier Pilod

Citations in the corpus

• Improvement of the energy method for strongly non resonant dispersive equations and applications (2014, unknown): “Now, part (2) will follow from general arguments (see for instance [10]).”
• Local Well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces (2008, background): “These l1-type X s,b structures were first introduced in [27] and used in [12,13,26,8].”
• Global well-posedness of Korteweg-de Vries equation in H^-3/4 (R) (2008, background): “We find that the bilinear estimates in F−3/4 almost hold except some potential logarithmic divergences from high× high→ low interactions.”