182 citations · 1.5k across the 227 of their papers we have counts for
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Strong solution for stochastic transport equations with irregular drift: existence and non-existence
Jinlong Wei, Jinqiao Duan, Hongjun Gao +1
We prove some existence, uniqueness and non-existence results of stochastic strong solutions for a class of stochastic transport equations with a -integrable (in time), bounded…
Existence and uniqueness of -solutions for stochastic transport equations
Jinlong Wei, Jinqiao Duan, Hongjun Gao +1
We investigate a stochastic transport equation driven by a multiplicative noise. For drift coefficient and …
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…
Kinetic solutions for nonlocal scalar conservation laws
Jinlong Wei, Jinqiao Duan, Guangying Lv
This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator. Ou…