Existence of weak solutions for two-phase matrix-valued harmonic map flows

2025/06/19 by Wang, Wei, Zhang, Zhifei · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.16278

Abstract

We investigate the existence of weak solutions for matrix-valued two-phase harmonic map flows with optimal lifespan, which arises as the limiting system of the matrix-valued Rubinstein-Sternberg-Keller problem studied by (\em Invent. Math., 233(1):1--80, 2023). Our approach employs a modified minimizing movement scheme, discretizing the time domain and constructing approximate solutions by interpolating solutions to the associated functional problem within each small time interval.

Citations

• Phase Transition of Parabolic Ginzburg--Landau Equation with Potentials of High-Dimensional Wells
• Matrix-valued Allen-Cahn equation and the Keller-Rubinstein-Sternberg problem
• Dynamics of the Nematic-Isotropic sharp interface for the liquid crystal

Cited by

• The sharp-interface limit of the matrix-valued Allen--Cahn equation

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