Abstract
The equatorial shallow water equations at low Froude number form a symmetric hyperbolic system with large terms containing a variable coefficient, the Coriolis parameter f, which depends on the latitude. The limiting behavior of the solutions as the Froude number tends to zero was investigated rigorously a few years ago, using the common approximation that the variations of f with latitude are linear. In that case, the large terms have a peculiar structure, due to special properties of the harmonic oscillator Hamiltonian, which can be exploited to prove strong uniform a priori estimates in adapted functional spaces. It is shown here that these estimates still hold when f deviates from linearity, even though the special properties on which the proofs were based have no obvious generalization. As in the linear case, existence, uniqueness and convergence properties of the solutions corresponding to general unbalanced data are deduced from the estimates.
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Communicated by L. Saint-Raymond
AlexandreDutrifoy is a research associate of the Fonds de la Recherche Scientifique - FNRS.
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Dutrifoy, A. Fast Averaging for Long- and Short-wave Scaled Equatorial Shallow Water Equations with Coriolis Parameter Deviating from Linearity. Arch Rational Mech Anal 216, 261–312 (2015). https://doi.org/10.1007/s00205-014-0808-z
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DOI: https://doi.org/10.1007/s00205-014-0808-z