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Type: Article
Damped wave equation with a critical nonlinearity in higher space dimensions
Abstract:
We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity vertical bar u vertical bar(2/n) u, where n denotes the space dimension. For n = 1,2,3, global in time existence of small solutions was shown in [4]. In this paper, we generalize the results to any spatial dimension via the method of decomposition of the equation into the high and low frequency components under the assumption that the initial data are small and decay rapidly at infinity. Furthermore we present a sharp time decay estimate of solutions with a logarithmic correction.
We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity vertical bar u vertical bar(2/n) u, where n denotes the space dimension. For n = 1,2,3, global in time existence of small solutions was shown in [4]. In this paper, we generalize the results to any spatial dimension via the method of decomposition of the equation into the high and low frequency components under the assumption that the initial data are small and decay rapidly at infinity. Furthermore we present a sharp time decay estimate of solutions with a logarithmic correction.
Journal: Journal of Mathematical Analysis and Applications
ISSN: 0022-247X
Year: 2017
Volume: 446
Number: 1
Pages: 801-822
Zbl Number: 06638942



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