7 papers · 1 filter
Sharp non-uniqueness of singular solutions to the one-dimensional periodic cubic nonlinear Schrödinger equation
Qirui Peng
We construct, via convex integration, a nonzero singular weak solution of the one-dimensional periodic cubic nonlinear Schrödinger equation that is compactly supported in time, has…
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 study the three-dimensional Electron Magnetohydrodynamics (EMHD) equations without resistivity, a regime known to be ill-posed in Sobolev and Gevrey spaces due to the quasilinea…
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…