Flow approach on Riesz type nonlocal energies

2025/05/26 by Jiaxin He, He, Jiaxin, Qinfeng Li +5
Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Nanofluid Flow and Heat Transfer

paper · pdf · doi:10.48550/arxiv.2505.19655

openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Via continuous deformations based on natural flow evolutions, we prove several novel monotonicity results for Riesz-type nonlocal energies on triangles and quadrilaterals. Some of these results imply new and simpler proofs for known theorems without relying on any symmetrization arguments.

Citations

• Flow approach on the monotonicity of shape functionals
• On the location of the maximal gradient of the torsion function over some non-symmetric planar domains
• The nonlocal isoperimetric problem for polygons: Hardy-Littlewood and Riesz inequalities
• Nonlinear Aggregation-Diffusion Equations: Radial Symmetry and Long Time Asymptotics
• Isoperimetric inequalities for eigenvalues of triangles

Related

• Minimizers of Nonlocal Polyconvex Energies in Nonlocal Hyperelasticity
• Continuous symmetrizations and uniqueness of solutions to nonlocal equations
• Flow approach on the monotonicity of shape functionals
• Explicit minimisers for anisotropic Riesz energies
• A Non-Local Mean Curvature Flow and its semi-implicit time-discrete approximation