MR2297944
Hoshiga, Akira
Akira HOSHIGA
The Existence of Global Solutions to Systems of Quasilinear Wave Equations with Quadratic Nonlinearities in 2-Dimensional Space
Funkcialaj Ekvacioj. Serio Internacia
49
2006
357--384
http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-3/49_357.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2297944
We deal with systems of quasilinear wave equations which contain quadratic nonlinearities in 2-dimensional space. We have already known that such the system has a smooth solution till the time $t_0=C\varepsilon^{-2}$ for sufficiently small $\varepsilon>0$, where $\varepsilon$ is the size of initial data. In this paper, we shall show that if quadratic and cubic nonlinearities satisfy so-called Null-condition, then the smooth solution exists globally in time. In the proof of the theorem, we use the Alinhac ghost weight energy.
Null-form, Multiple speeds, Global existence.
35A05, 35B45, 35L15.
49-357
2006
The Existence of Global Solutions to Systems of Quasilinear Wave Equations with Quadratic Nonlinearities in 2-Dimensional Space
HOSHIGA, Akira
Akira HOSHIGA
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