A particle scheme based on implicit Euler time stepping and spatial sampling is proved to converge for first-order MFGs under displacement monotonicity, handling non-separable Hamiltonians and singular data for arbitrary horizons.
Compact sets in the spaceLp(0, T;B)
10 Pith papers cite this work. Polarity classification is still indexing.
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Proves the standard observable package is insufficient for quantitative trace rates in NS one-component degeneration and states a conditional dichotomy on relaxed Schur visibility versus an NS-realizable left-singular cascade.
A new type of PDE for selective density-constrained crowd motion is obtained as the stiff limit of conservation laws, with existence of solutions proven via uniform BV estimates and compactness.
Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.
Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
Establishes a finite-scale estimate for filtered vortex stretching in 3D Navier-Stokes bounded by vorticity direction defects, absorbed by filtered diffusion, with far-field and commutator terms controlled via Carleson embeddings and cylindrical Young measures.
Establishes well-posedness in history space, Lipschitz and weak-star robustness, and compact global attractors with upper semicontinuity for semilinear reaction-diffusion equations with measure-valued delays.
Proves a conditional finite-scale reduction theorem deriving a lower bound on the regularity radius from smallness of the vertical velocity component under multiple structural assumptions for 3D Navier-Stokes.
The paper presents a conditional scale-critical defect-cascade reduction for the local regularity problem of the 3D incompressible Navier-Stokes equations that excludes invisible cascades to obtain CKN-scale regularity under structural hypotheses.
Audit of Navier-Stokes obstruction calculus shows existing decompositions locate CKN badness transport but lack coercive estimates, proving a resolution lemma and identifying the need for a filtered stretching-diffusion estimate with subgrid terms.
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Numerical analysis of first-order mean field games under displacement monotonicity
A particle scheme based on implicit Euler time stepping and spatial sampling is proved to converge for first-order MFGs under displacement monotonicity, handling non-separable Hamiltonians and singular data for arbitrary horizons.