110 citations · 484 across the 51 of their papers we have counts for
6 papers · 2 filters
Local Well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces
Zihua Guo
We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation \[\partial_t u+|\partial_x|^{1+α}\partial_x u+uu_x=0,\ u(x,0)=u_0(x),\] is locally well-posed…
Global Well-posedness of Korteweg-de Vries equation in
Zihua Guo
We prove that the Korteweg-de Vries initial-value problem is globally well-posed in and the modified Korteweg-de Vries initial-value problem is globally well-posed i…
Global well-posedness and limit behavior for the modified finite-depth-fluid equation
Zihua Guo, Baoxiang Wang
Considering the Cauchy problem for the modified finite-depth-fluid equation $\partial_tu-\G_δ(\partial_x^2u)\mp u^2u_x=0, u(0)=u_0$, where $\G_δf=-i \ft ^{-1}[\coth(2πδξ)-\frac{1}{…
Local Well-posedness and a priori bounds for the modified Benjamin-Ono equation without using a gauge transformation
Zihua Guo
We prove that the complex-valued modified Benjamin-Ono (mBO) equation is locally wellposed if the initial data belongs to for with $\normϕ_{L^2}$ sufficiently…
Global well posedness and inviscid limit for the Korteweg-de Vries-Burgers equation
Zihua Guo, Baoxiang Wang
Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation \begin{eqnarray*} u_t+u_{xxx}+ε|\partial_x|^{2α}u+(u^2)_x=0, \ u(0)=ϕ, \end{eqnarray*} where …
Decay estimates for a class of wave equations
Zihua Guo, Lizhong Peng, Baoxiang Wang
In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by , where is smooth aw…