A theorem of global existence of solutions to nonlinear wave equations in four space dimensions

DOI10.1007/BF01302932zbMath0718.35063OpenAlexW2066470083MaRDI QIDQ2639244

Jianmin Gao

Publication date: 1990

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178463

zbMATH Keywords

Cauchy problemglobal existencenonlinear wave equationssmallness

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Cites Work

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• The initial value problem for the equations of motion of viscous and heat-conductive gases
• Long-time behavior of solutions to nonlinear evolution equations
• 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
• A global existence theorem for the Cauchy problem of nonlinear wave equations
• Blow-up for quasi-linear wave equations in three space dimensions
• Remarks on the global sobolev inequalities in the minkowski space Rⁿ⁺¹

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