RESUMEN

This paper provides an error analysis for the Crank–Nicolson method of time discretization applied to spatially discrete Galerkin approximations of the nonstationary Navier–Stokes equations. Second-order error estimates are proven locally in time under realistic assumptions about the regularity of the solution. For approximations of an exponentially stable solution, these local error estimates are extended uniformly in time as t → ∞.

RESUMEN

We consider the system of dual-phase-lag thermoelasticity proposed by Chandrasekharaiah and Tzou. First, we prove that the solutions of the problem are generated by a semigroup of quasi-contractions. Thus, the problem of the third order in time is well-posed. Then the exponential stability is investigated. Finally the spatial behavior of solutions is analyzed in a semi-infinite cylinder and a result on the domain of influence is obtained.