Semi-discrete optimal transport methods for the semi-geostrophic equations

DOI10.1007/s00526-021-02133-zOpenAlexW3209155383WikidataQ114018060 ScholiaQ114018060MaRDI QIDQ2075806

Yanyan Li

Publication date: 16 February 2022

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.04430

zbMATH Keywords

incompressible semi-geostrophic equationsoptimal transport methodsrotational atmospheric flow

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Theoretical approximation in context of PDEs (35A35) Meteorology and atmospheric physics (86A10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Methods of ordinary differential equations applied to PDEs (35A24) PDEs in connection with geophysics (35Q86) Optimal transportation (49Q22) Transport equations (35Q49) Rossby waves (76U65)

Related Items (2)

A new implementation of the geometric method for solving the Eady slice equations ⋮ Entropic optimal transport solutions of the semigeostrophic equations

Cites Work

• A global existence result for the semigeostrophic equations in three dimensional convex domains
• On the Semi-Geostrophic system in physical space with general initial data
• A Lagrangian scheme à la Brenier for the incompressible Euler equations
• The semi-geostrophic system: weak-strong uniqueness under uniform convexity
• Classical solutions to semi-geostrophic system with variable Coriolis parameter
• Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure
• \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation
• Foundations of quantization for probability distributions
• Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case
• Convergence rates for discretized Monge-Ampère equations and quantitative stability of optimal transport
• Optimal transport: discretization and algorithms
• Fast methods for computing centroidal Laguerre tessellations for prescribed volume fractions with applications to microstructure generation of polycrystalline materials
• Smooth solutions of the surface semi-geostrophic equations
• Convergence of a Newton algorithm for semi-discrete optimal transport
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation
• The semigeostrophic equations discretized in reference and dual variables
• On Lagrangian Solutions for the Semi-geostrophic System with Singular Initial Data
• Weak stability of Lagrangian solutions to the semigeostrophic equations
• A Fully Nonlinear Version of the Incompressible Euler Equations: The Semigeostrophic System
• Centroidal Power Diagrams, Lloyd's Algorithm, and Applications to Optimal Location Problems
• A Numerical Algorithm forL₂Semi-Discrete Optimal Transport in 3D
• Weak Existence for the Semigeostrophic Equations Formulated as a Coupled Monge--Ampère/Transport Problem
• Existence of a weak solution for the semigeostrophic equation with integrable initial data
• Centroidal Voronoi Tessellations: Applications and Algorithms
• Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case
• Quantitative stability and error estimates for optimal transport plans
• Lagrangian Discretization of Crowd Motion and Linear Diffusion
• Hexagonal Patterns in a Simplified Model for Block Copolymers
• Hamiltonian ODEs in the Wasserstein space of probability measures
• Lagrangian Solutions of Semigeostrophic Equations in Physical Space
• Optimal Transport
• A variational approach for the 2-dimensional semi-geostrophic shallow water equations
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