TY - JOUR
T1 - Global existence for systems of quasilinear wave equations in (1 + 4)-dimensions
AU - Metcalfe, Jason
AU - Morgan, Katrina
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/2/15
Y1 - 2020/2/15
N2 - Hörmander proved global existence of solutions for sufficiently small initial data for scalar wave equations in (1+4)-dimensions of the form □u=Q(u,u′,u″) where Q vanishes to second order and (∂u 2Q)(0,0,0)=0. Without the latter condition, only almost global existence may be guaranteed. The first author and Sogge considered the analog exterior to a star-shaped obstacle. Both results relied on writing the lowest order terms u∂αu=1/2∂αu2 and as such do not immediately generalize to systems. The current study remedies such and extends both results to the case of multiple speed systems.
AB - Hörmander proved global existence of solutions for sufficiently small initial data for scalar wave equations in (1+4)-dimensions of the form □u=Q(u,u′,u″) where Q vanishes to second order and (∂u 2Q)(0,0,0)=0. Without the latter condition, only almost global existence may be guaranteed. The first author and Sogge considered the analog exterior to a star-shaped obstacle. Both results relied on writing the lowest order terms u∂αu=1/2∂αu2 and as such do not immediately generalize to systems. The current study remedies such and extends both results to the case of multiple speed systems.
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U2 - 10.1016/j.jde.2019.09.012
DO - 10.1016/j.jde.2019.09.012
M3 - Article
AN - SCOPUS:85072542680
SN - 0022-0396
VL - 268
SP - 2309
EP - 2331
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 5
ER -