In this work we study the lifespan of solutions to p-q system in the higher dimensional case n \geq 4. A suitable local existence curve in the p-q plane is found. The curve characterizes the local solutions in Sobolev space. Further, some lower and upper bounds of the lifespan of classical solutions are found too. The work is an extension of previous work, 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.
The lifespan of solutions to nonlinear systems of high dimensional wave equation
GUEORGUIEV, VLADIMIR SIMEONOV;
2006-01-01
Abstract
In this work we study the lifespan of solutions to p-q system in the higher dimensional case n \geq 4. A suitable local existence curve in the p-q plane is found. The curve characterizes the local solutions in Sobolev space. Further, some lower and upper bounds of the lifespan of classical solutions are found too. The work is an extension of previous work, 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.File in questo prodotto:
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