Decay of solutions to
a water wave model with a nonlocal viscous dispersive term
In this article, we investigate a
water wave model with a nonlocal viscous term
\begin{equation*}
u_t+u_x+\beta u_{xxx}+\frac{\sqrt{\nu}}{\sqrt{\pi}}\int_0^t
\frac{u_t(s)}{\sqrt{t-s}}ds+uu_x=\nu u_{xx}.
\end{equation*}
The wellposedness of the equation and
the decay rate of solutions
are investigated theoretically and numerically.
Min Chen (chen@math.purdue.edu)