Local Well-Posedness of a Two-Component Novikov System in Critical Besov Spaces
نویسندگان
چکیده
In this paper, we establish the local well-posedness for a two-component Novikov system in sense of Hadamard critical Besov spaces Bp,11+1p(R)×Bp,11+1p(R),1≤p<∞. We first provide uniform bound approximate solutions constructed by iterative scheme, then show convergence and regularity; afterwards, based on Lagrangian coordinate transformation techniques, prove uniqueness result; finally, that solution map is continuous.
منابع مشابه
Local Well-posedness and Blow-up Phenomenon for a Modified Two-component Camassa-Holm System in Besov Spaces
ρt + (uρ)x = 0, t > 0, x ∈ R, (1.1b) m(0, x) = m0(x), x ∈ R, (1.1c) ρ(0, x) = ρ0(x), x ∈ R, (1.1d) where (u0, ρ0) is given modified profile,m = u−uxx and ρ = (1−∂ x)(ρ−ρ0) ,g is a positive constant. For convenience, we let g = 1 in this paper. The modified two-component Camassa-Holm equation is written in terms of velocityu and locally averaged density ρ . With m = u− uxx ,ρ = γ − γxx and γ = ρ...
متن کاملGlobal well-posedness of the critical Burgers equation in critical Besov spaces
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
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 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 کاملOn well-posedness of the Cauchy problem for MHD system in Besov spaces
This paper studies the global well-posedness of solutions to the Cauchy problem of incompressible magneto-hydrodynamics system for large initial data in homogeneous Besov space Ḃ 2 p −1 p,r (R) for 2 < p < ∞ and 1 ≤ r < ∞. In the case of spatial dimension n ≥ 3 we establish the global well-posedness of solution for small data and the local one for large data in Besov space Ḃ n p −1 p,r (R), 1 ≤...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10071126