Decay of solutions to a viscous asymptotical model for waterwaves:
Kakutani–Matsuuchi model
In this article, we study a viscous asymptotical model equation for water
waves
$$u_t + u_x − βu_{txx} + ν(D^{1/2}u + F^{−1}(i|ξ|^{1/2}sgn(ξ)\hat{u}(ξ)))
+ γ uu_x = 0$$
proposed in Kakutani and Matsuuchi (1975) [6]. Theoretical questions
including the
existence and regularity of the solutions will be answered. Numerical
simulations of its
solutions will be carried out and the effects of various parameters will be
investigated. We
will also predict the decay rate of its solutions towards the equilibrium.
Min Chen (chen@math.purdue.edu)