TY - JOUR
T1 - Global existence for rough solutions of a fourth-order nonlinear wave equation
AU - Zhang, Junyong
PY - 2010/9
Y1 - 2010/9
N2 - In this paper, we prove that the cubic fourth-order wave equation is globally well-posed in Hs(Rn) for s > min {n-2/2,n/4} by following the Bourgain's Fourier truncation idea in Bourgain (1998) [2]. To avoid some troubles, we technically make use of the Strichartz estimate for low frequency part and high frequency part, respectively. As far as we know, this is the first result on the low regularity behavior of the fourth-order wave equation.
AB - In this paper, we prove that the cubic fourth-order wave equation is globally well-posed in Hs(Rn) for s > min {n-2/2,n/4} by following the Bourgain's Fourier truncation idea in Bourgain (1998) [2]. To avoid some troubles, we technically make use of the Strichartz estimate for low frequency part and high frequency part, respectively. As far as we know, this is the first result on the low regularity behavior of the fourth-order wave equation.
KW - Fourth-order wave equation
KW - Global well-posedness
KW - Low regularity
KW - Strichartz-type estimate
UR - http://www.scopus.com/inward/record.url?scp=77953024486&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2010.04.003
DO - 10.1016/j.jmaa.2010.04.003
M3 - Article
AN - SCOPUS:77953024486
SN - 0022-247X
VL - 369
SP - 635
EP - 644
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -