20 citations · 37 across the 16 of their papers we have counts for
21 papers
Well-posedness for a higher order water wave model on modulation spaces
Xavier Carvajal, Mahendra Panthee
Considered in this work is the initial value problem (IVP) associated to a higher order water wave model \begin{equation*} \begin{cases} η_t+η_x-γ_1 η_{xxt}+γ_2η_{xxx}+δ_1 η_{xxxxt…
Sharp global well-posedness for the cubic nonlinear Schrödinger equation with third order dispersion
Xavier Carvajal, Mahendra Panthee
We consider the initial value problem (IVP) associated to the cubic nonlinear Schrödinger equation with third-order dispersion \begin{equation*} \partial_{t}u+iα\partial^{2}_{x}u-…
On propagation of regularities and evolution of radius of analyticity in the solution of the fifth order KdV-BBM model
Xavier Carvajal, Mahendra Panthee
We consider the initial value problem (IVP) associated to a fifth order KdV-BBM type model that describes the propagation of unidirectional water waves. We prove that the regularit…
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(…
On the well-posedness, ill-posedness and norm-inflation for a higher order water wave model on a periodic domain
Xavier Carvajal, Mahendra Panthee, Ricardo Pastran
In this work we are interested in the well-posedness issues for the initial value problem associated with a higher order water wave model posed on a pe\-rio\-dic domain $\mathbb{T}…
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…