A note on quasilinear wave equations in two space dimensions

Dongbing  Zha

doi:10.3934/dcds.2016.36.2855

Article Contents

2016, Volume 36, Issue 5: 2855-2871. Doi: 10.3934/dcds.2016.36.2855

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A note on quasilinear wave equations in two space dimensions

Dongbing Zha^1,

1.
School of Mathematical Sciences, Fudan University, Shanghai 200433

Received: May 31, 2015

Revised: August 31, 2015

Published: May 2017

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Abstract

In this paper, we give an alternative proof of Alinhac's global existence result for the Cauchy problem of quasilinear wave equations with both null conditions in two space dimensions[S. Alinhac, The null condition for quasilinear wave equations in two space dimensions I, Invent. Math. 145 (2001) 597--618]. The innovation in our proof is that when applying the vector fields method to do the generalized energy estimates, we don't employ the Lorentz boost operator and only use the general space-time derivatives, spatial rotation and scaling operator.

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Mathematics Subject Classification: Primary: 35L05, 35L15; Secondary: 35L72.

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References

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