| Abstract: |
| In this talk, we will give the scattering of the mass-critical nonlinear Klein--Gordon equations both in the defocusing and focusing case(below the threshold) in higher dimensions. We establish the linear profile decomposition, then by using the solution of the mass-critical nonlinear Schr\odinger equation to approximate the large scale profile, we can prove the scattering of the solution of the nonlinear Klein-Gordon equation by the concentration-compactness/rigidity method developed by C. Kenig and F. Merle. We also study the behaviour of the solution of the focusing nonlinear Klein-Gordon equations around the threshold. |
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