2 papers
math.AP2020
Sharp well-posedness for a coupled system of mKdV type equations
Xavier Carvajal, Liliana Esquivel, Raphael Santos
We consider the initial value problem associated to a system consisting modified Korteweg-de Vries type equations $$ \partial_tv + \partial_x^3v + \partial_x(vw^2) =0,\ \ v(x,0)=ϕ(…
math.AP2019
Sharp ill-posedness and well-posedness results for dissipative KdV equations on the real line
Xavier Carvajal, Pedro Gamboa, Raphael Santos
This work is concerned about the Cauchy problem for the following generalized KdV- Burgers equation \begin{equation*} \left\{\begin{array}{l} \partial_tu+\partial_x^3u+L_pu+u\parti…