On global existence of solutions to nonlinear wave equations of wave map type

DOI10.1016/S0362-546X(99)00153-4zbMath0967.35096MaRDI QIDQ1586667

Masahito Ohta, Kenji Nakanishi

Publication date: 20 August 2001

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviourwell-posed problemill-posed problemblow-up of solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (2)

Small data wave maps in cyclic spacetime ⋮ Low regularity solutions for the wave map equation into the 2-D sphere

Cites Work

• The Cauchy problem for the O(N). CP(N-1), and GC(N,p) models
• Global existence of small solutions to nonlinear evolution equations
• Regularity results for nonlinear wave equations
• Global existence of low regularity solutions of nonlinear wave equations
• Smoothing estimates for null forms and applications
• On the regularity of spherically symmetric wave maps
• Global solutions of nonlinear hyperbolic equations for small initial data
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data
• Regularity of harmonic maps from the Minkowski space into rotationally symmetric manifolds
• Global existence for nonlinear wave equations
• Weak solutions and development of singularities of the SU(2) σ‐model
• Remarks on the blow-up boundaries and rates for nonlinear wave equations
• On the cauchy problem for equivariant wave maps
• Remark on the optimal regularity for equations of wave maps type
• Global existence of harmonic maps in minkowski space
• Global, small amplitude solutions to nonlinear evolution equations
• Counterexamples to Local Existence for Semi-Linear Wave Equations
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