On the blowup and lifespan of smooth solutions to a class of 2-D nonlinear wave equations with small initial data

DOI10.1090/S0033-569X-2015-01374-2zbMath1316.35204arXiv1110.0662OpenAlexW2963338836MaRDI QIDQ5254369

Ingo Witt, Yin Huicheng, Li Jun

Publication date: 9 June 2015

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.0662

zbMATH Keywords

Klainerman-Sobolev inequality

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Second-order quasilinear hyperbolic equations (35L72)

Related Items (3)

The small data solutions of general 3-D quasilinear wave equations. II. ⋮ On the lifespan and the blowup mechanism of smooth solutions to a class of 2-D nonlinear wave equations with small initial data ⋮ The almost global existence to classical solution for a 3-D wave equation of nematic liquid-crystals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the blowup of classical solutions to the 3-D pressure-gradient systems
• Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles
• The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space
• Blowup of small data solutions for a quasilinear wave equation in two space dimensions.
• Lectures on nonlinear hyperbolic differential equations
• The asymptotic behaviour of the radially symmetric solutions to quasilinear wave equations in two space dimensions
• Singularities of a variational wave equation
• Lifespan of solutions of semilinear wave equations in two space dimensions
• Global solutions of nonlinear hyperbolic equations for small initial data
• Initial value problems for nonlinear wave equations
• Dynamics of Director Fields
• Global solutions of nonlinear wave equations
• Remarks on the global sobolev inequalities in the minkowski space Rⁿ⁺¹
• The blowup of solutions for 3-D axisymmetric compressible Euler equations
• Existence of solutions to the transonic pressure gradient equations of the compressible euler equations in elliptic Regions
• On the second-order asymptotic equation of a variational wave equation
• Formation and construction of a shock wave for 3-D compressible Euler equations with the spherical initial data
• Global, small amplitude solutions to nonlinear evolution equations
• Energy Conservative Solutions to a One‐Dimensional Full Variational Wave System
• Global solutions of quasilinear wave equations
• On the lifespan of solutions of nonlinear wave equations with small initial data
• The null condition for quasilinear wave equations in two space dimensions. I

This page was built for publication: On the blowup and lifespan of smooth solutions to a class of 2-D nonlinear wave equations with small initial data