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In this paper, we study the supercritical aggregation equation. We prove the global well‐posedness for small initial data lying in Besov spaces and the local well‐posedness for arbitrary initial data. The Fourier localization technique and the Littlewood‐Paley theory are the main tools used in the proof.
Making use of the Fourier localization method, we prove the local‐in‐time existence and uniqueness of solutions to the viscous rotating shallow water equations with a term of capillarity under both the low regularity assumption on the initial data and the assumption that the initial height is bounded away from zero.
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