On the Nonlinear Variational Wave Equation

On the Nonlinear Variational Wave Equation

Mon, 17/10/2011
17:00 		Helge Holden (Norwegian University of Science and Technology) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
On the Nonlinear Variational Wave Equation
We prove existence of a global semigroup of conservative solutions of the nonlinear variational wave equation $ u_{tt}-c(u) (c(u)u_x)_x=0 $. The equation was derived by Saxton as a model for liquid crystals. This equation shares many of the peculiarities of the Hunter–Saxton and the Camassa–Holm equations. In particular, the equation possesses two distinct classes of solutions denoted conservative and dissipative. In order to solve the Cauchy problem uniquely it is necessary to augment the equation properly. In this talk we describe how this is done for conservative solutions. The talk is based on joint work with X. Raynaud.