TY - JOUR
T1 - Global well-posedness for 2D nonlinear wave equations without compact support
AU - Cai, Yuan
AU - Lei, Zhen
AU - Masmoudi, Nader
N1 - Publisher Copyright:
© 2017 Elsevier Masson SAS
PY - 2018/6
Y1 - 2018/6
N2 - In the significant work of [6], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the fact that the initial data have compact support [23]. Whether this constraint can be removed or not is still unclear. In this paper, for fully nonlinear wave equations under the null conditions, we prove the global well-posedness for small initial data without compact support. Moreover, we apply our result to a class of quasilinear wave equations.
AB - In the significant work of [6], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the fact that the initial data have compact support [23]. Whether this constraint can be removed or not is still unclear. In this paper, for fully nonlinear wave equations under the null conditions, we prove the global well-posedness for small initial data without compact support. Moreover, we apply our result to a class of quasilinear wave equations.
KW - Global well-posedness
KW - Null condition
KW - Two dimensional nonlinear wave equations
KW - Without compact support
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U2 - 10.1016/j.matpur.2017.09.011
DO - 10.1016/j.matpur.2017.09.011
M3 - Article
AN - SCOPUS:85033480640
SN - 0021-7824
VL - 114
SP - 211
EP - 234
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
ER -