The role of the dimension in uniqueness results for the stationary quasi-geostrophic system

2024/11/25 by Diego Chamorro, Chamorro, Diego, Manuel Fernando Cortez +1
Environmental Science · Earth and Planetary Sciences · #Methane Hydrates and Related Phenomena #Marine and environmental studies #Aquatic and Environmental Studies

paper · pdf · doi:10.48550/arxiv.2411.16414

Abstract

In this paper, we study a Liouville-type theorem for the stationary fractional quasi-geostrophic equation in various dimensions. Indeed, our analysis focuses on dimensions n = 2, 3, 4 and we explore the uniqueness of weak solutions for this fractional system. We demonstrate here that, under some specific Lebesgue integrability information, the only admissible solution to the stationary fractional quasi-geostrophic system is the trivial one and this result provides a comprehensive understanding of how the dimension in connection to the fractional power of the Laplacian influences the uniqueness properties of weak solutions.

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