2 papers
math.PR2025
McKean-Vlasov equations and nonlinear Fokker-Planck equations with critical singular Lorentz kernels
Michael Röckner, Deng Zhang, Guohuan Zhao
We prove the existence and conditional uniqueness in the Krylov class for SDEs with singular divergence-free drifts in the endpoint critical Lorentz space $L^{\infty}(0,T; L^{d,\in…
math.AP2021
Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations
Yachun Li, Zirong Zeng, Deng Zhang
We prove the non-uniqueness of weak solutions to 3D magnetohydrodynamic (MHD for short) equations. The constructed weak solutions do not conserve the magnetic helicity and can be c…