Now we will introduce some lemmas for the proof of the global existence theorem for the nonlinear wave equations with quadratic nonlinearities. The exsistence theorem which was proven before gives $n >5$ for the quadratic nonlinearities. But in fact this is not optimal. The theorem which will be introduced in the next seminars shows that $n > 3$ is sufficient for this case. To prove this, we have to apply some lemmas using Lorentz group operators in the Minkowski space.

2, Equation, Existence, Global, Group, invariance, Klainerman, Lorentz, M1, Minkowski, PDE, Quadratic, SDGE, Seminar, Space, Wave, WaveEquation, 파동방정식, 편미분방정식

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