Scattering and well-posedness for the Zakharov system at a critical space in four and more spatial dimensions.

zbMath1424.35314arXiv1512.00551MaRDI QIDQ2402130

Kotaro Tsugawa, Isao Kato

Publication date: 6 September 2017

Published in: Differential and Integral Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.00551

zbMATH Keywords

Banach fixed point theoremDuhamel principlebilinear estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (8)

Schrödinger-improved Boussinesq system in two space dimensions ⋮ Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in four and more spatial dimensions ⋮ Concentration compactness for the energy critical Zakharov system ⋮ The Zakharov system in dimension \(d \geq 4\) ⋮ A Note on C^2 Ill-posedness Results for the Zakharov System in Arbitrary Dimension ⋮ Zakharov system in two space dimensions ⋮ Local well-posedness for the Zakharov system in dimension \(d = 2, 3\) ⋮ Global well-posedness and scattering for the Zakharov system at the critical space in three spatial dimensions with small and radial initial data

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