Global existence without decay for quadratic Klein-Gordon equations

Abstract

The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering result is proven for small H^s data, s >= max(1/2, (n-2)/2), using the contraction mapping technique in U^2/V^2 based spaces. The result demonstrates that global results and scattering hold in this setting without the need to impose strong decay on the initial data.

22 pages

References in corpus (2)

• Well-posedness and scattering for the KP-II equation in a critical space
• Global existence for coupled Klein-Gordon equations with different speeds

Cited by in corpus (6)

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• Small data scattering for semi-relativistic equations with Hartree type nonlinearity
• Symplectic non-squeezing for the cubic nonlinear Klein-Gordon equation on ${\mathbb{T}}^3$
• Scattering for the quadratic Klein-Gordon equations
• Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and more dimensions
• Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in four and more spatial dimensions