Sharp well-posedness for a coupled system of mKdV type equations

2018/10/07 by Carvajal, Xavier, Panthee, Mahendra
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.03066

Abstract

We consider the initial value problem associated to a system consisting modified Korteweg-de Vries type equations \begincases ∂_tv + ∂_x³v + ∂_x(vw²) =0,amp;v(x,0)=ϕ(x),
∂_tw + α∂_x³w + ∂_x(v²w) =0,amp; w(x,0)=ψ(x), \endcases and prove the local well-posedness results for given data in low regularity Sobolev spaces H^s(ℝ)× H^s(ℝ), s> -\frac12, for 01 as well.

Related

• Sharp well-posedness for a coupled system of mKdV type equations
• Global Well-Posedness for a Coupled Modified KdV System
• Local well-posedness for a system of modified KdV equations in modulation spaces
• Sharp Global well-posedness for KdV and modified KdV on \R and \T
• KdV is wellposed in H^-1