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

Abstract

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 ${\dot{B}}_{p,1}^{\frac{1}{p}}(\mathbb{R})$ with $p\in [1,\infty )$, where $\Lambda =\sqrt{-△}$.

21pages

References in corpus (4)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Well-posedness of the Cauchy problem for the fractional power dissipative equations
• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
• On convergence of solutions of fractal Burgers equation toward rarefaction waves

Cited by in corpus (3)

• Regularity of solutions for the critical $N$-dimensional Burgers' equation
• On a one-dimensional α-patch model with nonlocal drift and fractional dissipation
• On the global well-posedness of a generalized 2D Boussinesq equations