The Quintic Nls on Perturbations of R3

Jao, Casey

doi:10.1353/ajm.2019.0026

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…For the nonlinear Schrödinger equation, the energy-critical problem for the defocusing quintic problem with initial data in the energy space for small, compactly supported perturbations of the Euclidean metric also exhibits scattering to linear solutions for all finite-energy data, as shown in [10]. There are many other known results for the energy-critical energy Schrödinger with potential, and for the exterior of a strictly convex obstacle, see [17,18,37], etc.…”

Section: ∂ |G| X 1+γmentioning

confidence: 94%

Scattering for critical wave equations with variable coefficients

Looi

Tohaneanu

2021

Proceedings of the Edinburgh Mathematical Society

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We prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to \infty$ , but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^{6}$ norm of the solution as $t\to \infty$ .

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Section: ∂ |G| X 1+γmentioning

confidence: 94%

Scattering for critical wave equations with variable coefficients

Looi

Tohaneanu

2021

Proceedings of the Edinburgh Mathematical Society

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“…For the nonlinear Schrödinger equation, the energy-critical problem for the defocusing quintic problem with initial data in the energy space for small, compactly supported perturbations of the Euclidean metric also exhibits scattering to linear solutions for all finite-energy data, as shown in [9]. In the exterior of a strictly convex obstacle, global well-posedness and scattering for all initial data in the energy space for the NLS was shown in [13].…”

Section: Introductionmentioning

confidence: 95%

Scattering for critical wave equations with variable coefficients

Looi¹,

Tohaneanu²

2019

Preprint

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We prove that solutions to the quintic semilinear wave equation with variable coefficients in R 1+3 scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as |x| → ∞, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the L 6 norm of the solution as t → ∞. Contents1. Introduction 2. Notation and Preliminaries 3. Energy conservation and local energy decay in Minkowski space 4. Uniform energy bounds and local energy decay for the nonlinear problem on perturbations 5. L 6 norm decay of solutions in Minkowski space 5.1. More notation 6. L 6 norm decay and scattering of solutions on small asymptotically flat perturbations of Minkowski space 6.1. L 6 norm decay of solutions on spacelike slices exterior to the cone 6.2. L 6 norm decay of solutions on interior spacelike slices of the cone 6.3. Scattering References

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