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Well-posedness and convergence of entropic approximation of semi-geostrophic equations

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arxiv 2404.17387 v1 pith:HPNYN3SJ submitted 2024-04-26 math.AP math-phmath.MPmath.OC

Guillaume Carlier , Hugo Malamut This is my paper · ORCID
classification math.APmath-phmath.MPmath.OC
keywords convergenceentropicequationssemi-geostrophicapproximationcomputeddiscretizationsestablish
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We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is also proved for discretizations that can be computed numerically in practice as shown recently in [6].

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  1. Entropic approximations of the semigeostrophic shallow water equations

    math.NA 2025-07 conditional novelty 5.0 of 10

    An entropy-regularized, Sinkhorn-based optimal transport discretization of the semigeostrophic shallow water equations is proposed, with a debiasing correction and numerical evidence of convergence.

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