TY - JOUR
T1 - The lifespan of solutions to nonlinear systems of a high-dimensional wave equation
AU - Georgiev, Vladimir
AU - Takamura, Hiroyuki
AU - Yi, Zhou
N1 - Funding Information:
The first author is partially supported by Research Training Network (RTN) HYKE, financed by the European Union, contract number : HPRN-CT-2002-00282. The second author is partially supported by Japanese Overseas Research Fellow (1/7/2002-30/6/2003) sponsored by Ministry of Education, Culture, Sports, Science and Technology in Japan. The third author is partially supported by Project 10225102 supported by NSFC.
PY - 2006/5/15
Y1 - 2006/5/15
N2 - In this work we study the lifespan of solutions to a p-q system in the higher-dimensional case n≥4. A suitable local existence curve in the p-q plane is found. The curve characterizes the local solutions in Sobolev space Hs with s≥0. Further, some lower and upper bounds of the lifespan of classical solutions are found too. This work is an extension of work [Geometric Optics and Related Topics, Progress in Nonlinear Differential Equations and their Applications, vol. 32, Birkhäuser, Basel, 1997, pp. 117-140], where a suitable global existence small data curve is studied. In the subcritical case, we give almost precise results for the lower bounds of the lifespan by using a suitable weighted Strichartz estimate for the higher-dimensional wave equation.
AB - In this work we study the lifespan of solutions to a p-q system in the higher-dimensional case n≥4. A suitable local existence curve in the p-q plane is found. The curve characterizes the local solutions in Sobolev space Hs with s≥0. Further, some lower and upper bounds of the lifespan of classical solutions are found too. This work is an extension of work [Geometric Optics and Related Topics, Progress in Nonlinear Differential Equations and their Applications, vol. 32, Birkhäuser, Basel, 1997, pp. 117-140], where a suitable global existence small data curve is studied. In the subcritical case, we give almost precise results for the lower bounds of the lifespan by using a suitable weighted Strichartz estimate for the higher-dimensional wave equation.
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U2 - 10.1016/j.na.2005.08.012
DO - 10.1016/j.na.2005.08.012
M3 - Article
AN - SCOPUS:33644882269
SN - 0362-546X
VL - 64
SP - 2215
EP - 2250
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 10
ER -