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Dispersive effects of weakly compressible and fast rotating inviscid fluids

  • * Corresponding author: Van-Sang Ngo

    * Corresponding author: Van-Sang Ngo 

The research of the second author was partially supported by the Basque Government through the BERC 2014-2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa accreditation SEV-2013-0323

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  • We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $ H^s \left( \mathbb{R}^3 \right), s>5/2 $. We prove that the system admits a unique local strong solution in $ L^\infty \left( [0,T]; H^s\left( \mathbb{R}^3 \right) \right) $, where $ T $ is independent of the Rossby and Mach numbers. Moreover, using Strichartz-type estimates, we prove the longtime existence of the solution, i.e. its lifespan is of the order of $\varepsilon^{-\alpha}, \alpha >0$, without any smallness assumption on the initial data (the initial data can even go to infinity in some sense), provided that the rotation is fast enough.

    Mathematics Subject Classification: 35A01, 35A02, 35Q31, 76N10, 76U05.


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