2 citations · 7 across the 12 of their papers we have counts for
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The Cauchy problem for the generalized KdV equation with rough data and random data
Wei Yan, Xiangqian Yan, Jinqiao Duan +1
In this paper, we consider the Cauchy problem for the generalized KdV equation with rough data and random data. Firstly, we prove that as $t\longrigh…
New lower bounds on the radius of spatial analyticity for the KdV equation
Jianhua Huang, Ming Wang
The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than as time goes to in…
The Cauchy problem for two dimensional generalized Kadomtsev-Petviashvili-I equation in anisotropic Sobolev spaces
Wei Yan, Yongsheng Li, Jianhua Huang +1
The goal of this paper is three-fold. Firstly, we prove that the Cauchy problem for generalized KP-I equation \begin{eqnarray*} u_{t}+|D_{x}|^α\partial_{x}u+\partial_{x}^{-1}\parti…
Random data Cauchy problem for a generalized KdV equation in the supercritical case
Wei Yan, Jinqiao Duan, Jianhua Huang
We consider the Cauchy problem for a generalized KdV equation \begin{eqnarray*} u_{t}+\partial_{x}^{3}u+u^{7}u_{x}=0, \end{eqnarray*} with random data on \R. Kenig, Ponce, Vega(Com…
Random data Cauchy problem for the wave equation on compact manifold
Jinqiao Duan, Jianhua Huang, Yongsheng Li +1
Inspired by the work of Burq and Tzvetkov (Invent. math. 173(2008), 449-475.), firstly, we construct the local strong solution to the cubic nonlinear wave equation with random data…
Sharp well-posedness and ill-posedness of the Cauchy problem for the higher-order KdV
Wei Yan, Minjie Jiang, Yongsheng Li +1
In this paper, we investigate the Cauchy problem for the higher-order KdV-type equation \begin{eqnarray*} u_{t}+(-1)^{j+1}\partial_{x}^{2j+1}u + \frac{1}{2}\partial_{x}(u^{2}) = 0,…
Well-posedness for Stochastic Generalized Fractional Benjamin-Ono Equation
Wei Yan, Jianhua Huang, Boling Guo
This paper is devoted to the Cauchy problem for the stochastic generalized Benjamin-Ono equation. By using the Bourgain spaces and Fourier restriction method and the assumption tha…
The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity
Yongsheng Li, Jianhua Huang, Wei Yan
In this paper, we investigate the Cauchy problem for the Ostrovsky equation \begin{eqnarray*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\frac{1}{2}\partial_{x}(u^{2})\right) -γu=…