Global well-posedness of the critical Burgers equation in critical Besov spaces
نویسندگان
چکیده
We make use of the method of modulus of continuity [7] and Fourier localization technique [1] to prove the global well-posedness of the critical Burgers equation ∂tu + u∂xu + Λu = 0 in critical Besov spaces Ḃ 1 p p,1(R) with p ∈ [1,∞), where Λ = √ −△. 2000 Mathematics Subject Classification: 35K55, 35Q53
منابع مشابه
On the Global Solutions of the Super-critical 2d Quasi-geostrophic Equation in Besov Spaces
In this paper we study the super-critical 2D dissipative quasi-geostrophic equation. We obtain some regularization effects allowing us to prove global well-posedness result for small initial data lying in critical Besov spaces constructed over Lebesgue spaces L, with p ∈ [1,∞]. Local results for arbitrary initial data are also given.
متن کاملGlobal well-posedness for the 3D incompressible inhomogeneous Navier-Stokes equations and MHD equations
The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work by Abidi, Gui and Zhang (Arch. Ration. Mech. Anal. 204 (1):189–230, 2012, and J. Math. Pures Appl. 100 (1):166–203, 2013) to a more lower regularity index a...
متن کاملOn the Global Well-Posedness of the Critical Quasi-Geostrophic Equation
We prove the global well-posedness of the critical dissipative quasi-geostrophic equation for large initial data belonging to the critical Besov space Ḃ ∞,1(R ).
متن کاملOn the well-posedness of the full low-Mach number limit system in general critical Besov spaces
This work is devoted to the well-posedness issue for the low-Mach number limit system obtained from the full compressible Navier-Stokes system, in the whole space R with d ≥ 2. In the case where the initial temperature (or density) is close to a positive constant, we establish the local existence and uniqueness of a solution in critical homogeneous Besov spaces of type Ḃ p,1. If, in addition, t...
متن کاملGlobal well-posedness of incompressible flow in porous media with critical diffusion in Besov spaces
In this paper we study the model of heat transfer in a porous medium with a critical diffusion. We obtain global existence and uniqueness of solutions to the equations of heat transfer of incompressible fluid in Besov spaces Ḃ 3/p p,1 (R ) with 1 ≤ p ≤ ∞ by the method of modulus of continuity and Fourier localization technique. AMS Subject Classification 2000: 76S05, 76D03
متن کامل