Explicit self-similiar singularity of Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation

2017/12/14 by Weiping Yan, Yan, Weiping · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1712.05159

openalex publication_date 2017/12/14 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28

Abstract

This paper studies the self-similar singularity phenomenon of zero mean curvature equation including Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation which arises in string theory and geometric minimal surfaces theory. We show that there exist new explicit self-similar solutions for Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation in Minkowski space R¹⁺³ with respect to the radially symmetric case.

Cited by

• On the explicit blowup solutions for 3D incompressible Magnetohydrodynamics equations
• Finite time blowup explicit solution for 3D incompressible Euler equations

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