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We prove Strichartz estimates for the semigroups associated to stratifiedand/or rotating inviscid geophysical fluids using Fourier restriction theory.We prove new results for rotating stratified fluids, and recover results from[16] for rotation only, and from [17] for stratification only. Our restrictionestimates are obtained by the slicing method [20], which relies on thewell-known Tomas-Stein theorem for 2-dimensional spheres. To our knowledge,such a method has never been used in this setting. Moreover, when the fluid isstratified, our approach yields sharp estimates, showing that the slicingmethod captures all the available curvature of the surfaces of interest.

Strichartz estimates for geophysical fluid equations using Fourier restriction theory