Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition

Abstract

The paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition utt-Δu+Δ2u-Δut-Δg(u)=f(x). The main result is concerned with nonlinearities g(u) with supercritical growth. In that case, we construct a bounded absorbing set with further regularity and obtain quasi-stability estimates. Then the exponential attractor is established in natural energy space V2×H.