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Long time decay for 2D Klein-Gordon equation. (English) Zbl 1192.35151

Summary: We obtain a dispersive long-time decay in weighted energy norms for solutions of the 2D Klein-Gordon equations. The decay extends the results obtained by Jensen, Kato and Murata for the equations of Schrödinger type by the spectral approach. For the proof, we modify the approach to make it applicable to relativistic equations.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q40 PDEs in connection with quantum mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35B40 Asymptotic behavior of solutions to PDEs
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