Recent works on the Strauss conjecture

Abstract

In this review paper, we summarize the current state-of-art on the Strauss conjecture with nontrapping obstacles. Among others, three essential estimates are emphasized and presented: Morawetz-KSS estimates (also known as local energy estimates), weighted Strichartz estimates and generalized Strichartz estimates.

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References in corpus (5)

• Some Remarks on Strichartz Estimates for Homogeneous Wave Equation
• Generalized and weighted Strichartz estimates
• Concerning the Strauss conjecture on asymptotically Euclidean manifolds
• Almost global existence for some semilinear wave equations with almost critical regularity
• The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions

Cited by in corpus (8)

• The Strauss conjecture on Kerr black hole backgrounds
• Challenges to global solutions in Horndeski's theory
• Long time existence for semilinear wave equations on asymptotically flat space-times
• The Strauss conjecture on asymptotically flat space-times
• Global existence and lifespan for semilinear wave equations with mixed nonlinear terms
• Blow-up for Strauss type wave equation with damping and potential
• The Strauss conjecture on negatively curved backgrounds
• Blow up for small-amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds