Global well-posedness and inviscid limit for the modified Korteweg–de Vries–Burgers equation Original Research Article

Considering the Cauchy problem for the modified Korteweg–de Vries–Burgers equation View the MathML sourceut+uxxx+ϵ|∂x|2αu=2(u3)x,u(0)=ϕ, Turn MathJax on where 0<ϵ,α≤10<ϵ,α≤1 and uu is a real-valued function, we show that it is uniformly globally well-posed in View the MathML sourceHs(s≥1) for all ϵ∈(0,1]ϵ∈(0,1]. Moreover, we prove that for any s≥1s≥1 and T>0T>0, its solution converges in View the MathML sourceC([0,T];Hs) to that of the MKdV equation if ϵϵ tends to 0.