The local well-posedness and global solution for a modified periodic two-component Camassa–Holm system
نویسندگان
چکیده
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 کاملSharp Global Well - Posedness for Kdv and Modified Kdv On
The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all L 2-based Sobolev spaces H s where local well-posedness is presently known, apart from the H 1 4 (R) endpoint for mKdV. The result for KdV relies on a new method for co...
متن کاملGlobal Well-posedness of Nls-kdv Systems for Periodic Functions
We prove that the Cauchy problem of the Schrödinger-KortewegdeVries (NLS-KdV) system for periodic functions is globally well-posed for initial data in the energy space H1×H1. More precisely, we show that the nonresonant NLS-KdV system is globally well-posed for initial data in Hs(T) × Hs(T) with s > 11/13 and the resonant NLS-KdV system is globally wellposed with s > 8/9. The strategy is to app...
متن کاملGlobal Well-posedness for Periodic Generalized Korteweg-de Vries Equation
In this paper, we show the global well-posedness for periodic gKdV equations in the space H(T), s ≥ 1 2 for quartic case, and s > 5 9 for quintic case. These improve the previous results of Colliander et al in 2004. In particular, the result is sharp in the quartic case.
متن کاملA ug 2 00 8 Low regularity global well - posedness for the two - dimensional Zakharov system ∗
The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L-norm of the Schrödinger part is small enough. The proof uses a refined I-method originally initiated by Colliander, Keel, Staffilani, Takaoka and Tao. A polynomial growth bound for the solution is also given.
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: Journal of Mathematical Analysis and Applications
سال: 2014
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.12.018