Exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition (Q2314723)

Summary: The paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition \(u_{t t} - \Delta u + \Delta^2 u - \Delta u_t - \Delta g(u) = f(x)\). 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 \(V_2 \times H\).