Global versions of the Gagliardo-Nirenberg-Sobolev inequality and applications to wave and Klein-Gordon equations

In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition that allows us to prove the global nonlinear asymptotic stability of the plane wave. The proof of global stability requires us to analyze the geometry of the interaction between the background plane wave and the perturbation. When this condition is not met, we are able to prove linear instability assuming an additional genericity condition. The linear instability is shown using a geometric optics ansatz.

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Global versions of the Gagliardo-Nirenberg-Sobolev inequality and applications to wave and Klein-Gordon equations

Cited by 2 publications

References 3 publications

Global stability of some totally geodesic wave maps

Global stability of some totally geodesic wave maps

Stability and Instability of Traveling Wave Solutions to Nonlinear Wave Equations

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