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摘要
In this paper, we prove scattering for the defocusing Beam equation partial derivative(2)(t)u + Delta(2)u + mu + lambda vertical bar u vertical bar(p-1)u = 0 in low dimensions 2 <= n <= 4 for p > 1 + 8/n and lambda > 0. The main difficulty is the absence of a Morawetz-type estimate and of a Galilean transformation in order to be able to control the Momentum vector. We overcome the former by using a strategy derived from concentration-compactness ideas, and the latter by considering a Virial-type identity in the direction orthogonal to the Momentum vector.
- 出版日期2010
