Abstract
The paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary conditionutt-Δu+Δ2u-Δut-Δg(u)=f(x). The main result is concerned with nonlinearitiesg(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 spaceV2×H.
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