Roberta Bianchini* and Roberto Natalini

IAC, Consiglio Nazionale delle Ricerche,
Rome, Italy.

This article deals with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined with bilinear estimates and interpolation inequalities for handling the nonlinearity.

Mathematics Subject Classification: 35Q35 / 35B40

Key words: Stratified fluids / Boussinesq approximation / Green function analysis / dispersion relation homogeneous of degree 0 / anisotropic decay rates

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