Resumen de Global solutions and blow-up phenomena for the periodic b-equation

S. Zhang, Zhaoyang Yin

• In the paper, we mainly study the Cauchy problem of a family of asymptotically equivalent shallow water wave equations, the so called periodic b-equation. We first establish the local wellposedness for the periodic b-equation. Then we derive the precise blow-up scenario and present two blow-up results. Moreover, we show that the periodic b-equation has global strong solutions.

  Finally, we prove the existence of global weak solutions to the periodic b-equation, provided that initial data satisfy certain sign conditions