Local well-posedness for third order Benjamin-Ono type equations on the torus

2018/12/09 by Tanaka, Tomoyuki
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.03477

Abstract

We consider the Cauchy problem of third order Benjamin-Ono type equations on the torus. Nonlinear terms may yield derivative losses, which prevents us from using the classical energy method. In order to overcome that difficulty, we add a correction term into the energy. We also use the Bona-Smith type argument to show the continuous dependence.

Related

• Local well-posedness for fourth order Benjamin-Ono type equations
• The third order Benjamin-Ono equation on the torus : well-posedness, traveling waves and stability
• On the L² well-posedness and decay estimate of third order Benjamin-Ono equation
• Sharp well-posedness results of the Benjamin-Ono equation in H^s(\mathbbT,ℝ) and qualitative properties of its solution
• On the flow map of the Benjamin-Ono equation on the torus