On the Cauchy problem for a nonlinearly dispersive wave equation

Details On the Cauchy problem for a nonlinearly dispersive wave equation On the Cauchy problem for a nonlinearly dispersive wave equation

2003-09-10

arxiv.org/abs/math/0309183v1

J. Nonlinear Math. Phys., volume 10, no. 1 (2003) 10-15

Mathematics

Analysis of PDEs

arxiv version is already official

Scientific paper

We establish the local well-posedness for a new nonlinearly dispersive wave
equation and we show that the equation has solutions that exist for indefinite
times as well as solutions which blowup in finite times. Furthermore, we derive
an explosion criterion for the equation and we give a sharp estimate from below
for the existence time of solutions with smooth initial data.

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