In this talk we are concerned with the well-posedness of the initial value problem to a shallow water model for two-dimensional water waves with a floating solid body. We consider three cases: the body is fixed, the motion of the body is prescribed, and the body moves freely according to Newton's laws. The difficulty of the analysis comes from the fact that we have to treat the contact points, where the water, the air, and the solid body meet. This model yields a new type of free boundary problems for a quasilinear hyperbolic system. We will report that the initial value problem to this model is in fact well-posed. This result is based on the joint research with David Lannes at University of Bordeaux.

• 世話人：
  • 立川 篤 (東京理科大学理工学部数学科)
  • 山崎 多恵子　(東京理科大学理工学部数学科)
  • 牛島 健夫　(東京理科大学理工学部数学科)
  • 相木 雅次　(東京理科大学理工学部数学科)
  • 側島 基宏　(東京理科大学理工学部数学科)
  • 若狭 恭平　(東京理科大学理工学部数学科)