Keio Univ. Yagami-campus, Building 14, Room 631 A/B
3-14-1 Kouhoku-ku, Hiyoshi, Yokohama 223-8522, JAPAN
Speaker: Tomoyuki Tanaka
Title: Local well-posedness for third order Benjamin-Ono type equations on the torus
Abstract:
In this talk, we consider the Cauchy problem of third order Benjamin-Ono type equations on the torus.
The well-known (second order) Benjamin-Ono equation describes the behavior of long internal waves in deep stratified fluids.
This equation also has infinitely many conservation laws, which generates a hierarchy of Hamiltonian equations of order j.
Our equation with specific coefficients is known as the second equation in the Benjamin-Ono hierarchy.
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.
This talk is based on the preprint titled the same as above (arXiv:1812.03477) by the speaker.
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