32 citations · 84 across the 11 of their papers we have counts for
10 papers · 1 filter
On self-similar singular solutions to a vorticity stretching equation
Dapeng Du, Jingyu Li, Xinyue Shi
We consider the following model equation: \begin{equation} ω_{t} = Z_{11}ω\,ω, \end{equation} where \begin{equation} Z_{11} = \partial_{11}Δ^{-1} \end{equation} is a Calderon-Zygmo…
Global solutions to the Nernst-Planck-Euler system on bounded domain
Dapeng Du, Jingyu Li, Yansheng Ma +1
We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded do…
On some model equations of Euler and Navier-Stokes equations
Dapeng Du
We propose a two-dimensional generalization of Constantin-Lax-Majda model [2]. Some results about singular solutions are given. This model might be the first step toward the singul…
On Blow-up criterion for the Nonlinear Schrödinger Equation
Dapeng Du, Yifei Wu, Kaijun Zhang
The blowup is studied for the nonlinear Schrödinger equation with is odd and (the energy-critical or energy-supercritical case).…
Partial Regularity of solutions to the Four-Dimensional Navier-Stokes Equations
Hongjie Dong, Xumin Gu
In this paper, we consider suitable weak solutions of incompressible Navier--Stokes equations in four spatial dimensions. We prove that the two-dimensional time-space Hausdorff mea…
Blowup of Smooth Solutions to the Navier-Stokes Equations for Compressible Isothermal Fluids
Du Dapeng, Li Jingyu, Zhang Kaijun
It is shown that the one-dimensional or two-dimensional radially symmetric isothermal compressible Navier-Stokes system has no non-trivial global smooth solutions if the initial de…