论文标题
三个及更高维
Scattering for the mass-critical nonlinear Klein-Gordon equations in three and higher dimensions
论文作者
论文摘要
在本文中，我们考虑了三个和更高维度的实价质量批判性非线性klein-gordon方程。我们证明，在聚焦案例中，散射和爆炸之间的二分法与散落情况下的能量散射。我们将浓度 - 乳胶/刚度法作为R. Killip，B。Stovall和M. Visan [Trans。阿米尔。数学。 Soc。 364（2012）]。主要的新颖性是当非线性不是代数时，通过质量批判性非线性Schrödinger方程的解决方案近似大规模（低频）曲线。
In this paper we consider the real-valued mass-critical nonlinear Klein-Gordon equations in three and higher dimensions. We prove the dichotomy between scattering and blow-up below the ground state energy in the focusing case, and the energy scattering in the defocusing case. We use the concentration-compactness/rigidity method as R. Killip, B. Stovall, and M. Visan [Trans. Amer. Math. Soc. 364 (2012)]. The main new novelty is to approximate the large scale (low-frequency) profile by the solution of the mass-critical nonlinear Schrödinger equation when the nonlinearity is not algebraic.
