7 papers · 1 filter
Sharp non-uniqueness of singular solutions to the one-dimensional periodic cubic nonlinear Schrödinger equation
Qirui Peng
We construct by convex integration a nonzero singular weak solution of the one-dimensional periodic cubic nonlinear Schrödinger equation that is compactly supported in time, has ze…
Onsager-Type Energy Equality and Prodi--Serrin Uniqueness for Nernst--Planck Fluid Systems
Ruimeng Hu, Quyuan Lin, Qirui Peng
We study weak solutions of electrodiffusion systems coupling the Nernst--Planck equations with fluid models. First, for the three-dimensional Nernst--Planck--Euler system, we estab…
Local well-posedness for the two-and-a-half-dimensional EMHD system with split fractional dissipation
Qirui Peng
We study the -dimensional electron magnetohydrodynamics (EMHD) system on with componentwise fractional dissipation: and $…
Anomalous Dissipation at Onsager-Critical Regularity
Alexey Cheskidov, Qirui Peng
We construct solutions to the three-dimensional Euler equations exhibiting anomalous dissipation in finite time through a vanishing viscosity limit. Inspired by \cite{BDL23} and \c…
Well-posedness of the relaxed Electron MHD equations with random diffusion
Ruimeng Hu, Qirui Peng, Xu Yang
We investigate a three-dimensional active-vector relaxation of the electron magnetohydrodynamics (EMHD) equations without resistivity. The relaxation replaces the electron current…
Three dimensional stationary solutions of the Electron MHD equations
Qirui Peng
The goal of this paper is to construct non-trivial steady-state weak solutions of the three dimensional Electron Magnetohydrodynamics equations in the class of f…
An optimal upper bound on the determining wavenumber for 3D Navier-Stokes Equations
Alexey Cheskidov, Qirui Peng
We introduce a determining wavenumber for weak solutions of 3D Navier-Stokes equations whose time average is bounded by Kolmogorov dissipation wavenumber over the whole range of in…