Global well-posedness of the critical Burgers equation in critical Besov spaces

Details Global well-posedness of the critical Burgers equation in critical Besov spaces Global well-posedness of the critical Burgers equation in critical Besov spaces

2008-05-22

arxiv.org/abs/0805.3465v3

J. Differential Equations, 247(2009)1673-1693

Mathematics

Analysis of PDEs

21pages

Scientific paper

10.1016/j.jde.2009.03.028

We make use of the method of modulus of continuity \cite{K-N-S} and Fourier
localization technique \cite{A-H} to prove the global well-posedness of the
critical Burgers equation $\partial_{t}u+u\partial_{x}u+\Lambda u=0$ in
critical Besov spaces $\dot{B}^{\frac{1}{p}}_{p,1}(\mathbb{R})$ with
$p\in[1,\infty)$, where $\Lambda=\sqrt{-\triangle}$.

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