caa a22 4500 605514941 CHVBK 20210128100706.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00205-014-0808-z doi (NATIONALLICENCE)springer-10.1007/s00205-014-0808-z Dutrifoy Alexandre Université Libre de Bruxelles, Campus Plaine, CP 214, Bd du Triomphe, 1050, Brussels, Belgium aut Fast Averaging for Long- and Short-wave Scaled Equatorial Shallow Water Equations with Coriolis Parameter Deviating from Linearity [Elektronische Daten] [Alexandre Dutrifoy] 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. Springer-Verlag Berlin Heidelberg, 2014 Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 261-312 0003-9527 216:1<261 2015 216 205 https://doi.org/10.1007/s00205-014-0808-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0808-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dutrifoy Alexandre Université Libre de Bruxelles, Campus Plaine, CP 214, Bd du Triomphe, 1050, Brussels, Belgium aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 261-312 0003-9527 216:1<261 2015 216 205