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math.AP2026
Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous
Zhenyu Wan, Weikui Ye, Zhaoyang Yin
This paper is concerned with the Cauchy problem for the 3D incompressible magnetohydrodynamic (MHD) equations in supercritical Sobolev spaces. It is well known that the system is l…
math.AP2026
Global conservative weak solutions and global strong solutions for a class of weakly dissipative nonlinear dispersive wave equations
Yiyao Lian, Zhenyu Wan, Zhaoyang Yin
In this paper, we study the global existence of solutions of the Cauchy problem for a class of weakly dissipative nonlinear dispersive wave equations $u_t-u_{xxt}+(f\left(u\right))…