Yingbo LIU
,
Ingo WITT
. SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS[J]. Acta mathematica scientia, Series B, 2018
, 38(1)
: 125
-150
.
DOI: 10.1016/S0252-9602(17)30121-2
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satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation (∂t2-△x)u+
satisfying null conditions with small initial data and the coefficients depending simultaneously on u and ∂u. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.