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math.AP2026
Existence of weak solutions and regular solutions to the incompressible Schrödinger flow
Bo Chen, Guangwu Wang, Youde Wang
In this paper, we are concerned with the initial-Neumann boundary value problem of the Schrödinger flow for maps from a smooth bounded domain in an Euclidean space into $\mathbb{S}…
math.AP2026
Global existence of weak solutions for Landau-Lifshitz equation with helical derivatives
Bo Chen, Zhen Qiu
In this paper, we investigate the chiral boundary value problem for the Landau-Lifshitz equation with helical derivatives. By introducing Sobolev spaces adapted to the helical deri…
math.AP2026
Novel Self-similar Finite-time Blowups with Singular Profiles of the 1D Hou-Luo Model and the 2D Boussinesq Equations: A Numerical Investigation
Bojin Chen, De Huang, Xiangyuan Li
We present novel self-similar finite-time blowup scenarios for the 1D Hou--Luo model. We numerically demonstrate that solutions that initially satisfy certain derivative degeneracy…