Flow approach on Riesz type nonlocal energies
Jiaxin He, Qinfeng Li, Juncheng Wei, Hang Yang
TL;DR
This paper introduces a flow-based method to analyze Riesz-type nonlocal energies, establishing new monotonicity results on polygons and providing simpler proofs for existing theorems.
Contribution
It presents a novel flow approach to study nonlocal energies, leading to new monotonicity results and simplified proofs without symmetrization.
Findings
New monotonicity results for Riesz-type energies on polygons
Simplified proofs of known theorems using flow methods
Potential for broader application of flow techniques in nonlocal energy analysis
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.
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Taxonomy
TopicsLattice Boltzmann Simulation Studies · Fluid Dynamics and Turbulent Flows · Nanofluid Flow and Heat Transfer