Differential and Integral Equations

Small-data scattering for nonlinear waves of critical decay in two space dimensions

Paschalis Karageorgis and Kimitoshi Tsutaya

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Abstract

Consider the nonlinear wave equation with zero mass in two space dimensions. When it comes to the associated Cauchy problem with small initial data, the known existence results are already sharp; those require the data to decay at a rate $k\geq k_c$, where $k_c$ is a critical decay rate that depends on the order of the nonlinearity. However, the known scattering results treat only the supercritical case $k>k_c$. In this paper, we prove the existence of the scattering operator for the full optimal range $k\geq k_c$.

Article information

Source
Differential Integral Equations, Volume 19, Number 6 (2006), 601-626.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050355

Mathematical Reviews number (MathSciNet)
MR2234716

Zentralblatt MATH identifier
1212.35274

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35P25: Scattering theory [See also 47A40]

Citation

Karageorgis, Paschalis; Tsutaya, Kimitoshi. Small-data scattering for nonlinear waves of critical decay in two space dimensions. Differential Integral Equations 19 (2006), no. 6, 601--626. https://projecteuclid.org/euclid.die/1356050355


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