Nonlinear stability of explicit self-similar solutions for the timelike extremal hypersurfaces in \(\mathbb{R}^{1+3}\)

DOI10.1007/s00526-020-01798-2zbMath1448.35070arXiv1907.01126OpenAlexW3040935242MaRDI QIDQ786068

Weiping Yan

Publication date: 12 August 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.01126

zbMATH Keywords

Minkowski spacetimeNewton's polygontimelike extremal hypersurfaces

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) PDEs in connection with relativity and gravitational theory (35Q75) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12) Self-similar solutions to PDEs (35C06)

Related Items (12)

The inviscid limit for the incompressible stationary magnetohydrodynamics equations in three dimensions ⋮ Asymptotic stability of explicit blowup solutions for three-dimensional incompressible magnetohydrodynamics equations ⋮ Construction of a family of stable finite-time blowup solutions for the viscous Boussinesq system ⋮ Asymptotic stability of stationary solutions for the Kirchhoff equation ⋮ Stabilization for the Klein–Gordon–Zakharov system ⋮ Asymptotic stability of explicit infinite energy blowup solutions of the 3D incompressible Navier-Stokes equations ⋮ Global stability dynamics of the timelike extremal hypersurfaces in Minkowski space ⋮ Stabilizability for a Quasilinear Klein–Gordon-Wave System with Variable Coefficients ⋮ Global stability dynamics of the quasilinear damped Klein-Gordon equation with variable coefficients ⋮ The inviscid limit for the steady incompressible Navier-Stokes equations in the three dimension ⋮ Global small finite energy solutions for the incompressible magnetohydrodynamics equations in \(\mathbb{R}^+ \times \mathbb{R}^2\) ⋮ Sobolev regularity solutions for a class of singular quasilinear ODEs

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