PreprintCC BY 4.0arXiv
A Differential Algebraic Framework for Boundary Layer α-Models
Abstract
By addressing the problem of describing the differences between the saturation monoids of the Prandtl and Leray-α boundary layers, and algebraically distinguishing the action of the Helmholtz operator, we can show that, when the modification of the vector field is halted at a minimum scale determined by the differential filter, the paradox of constructing a solution that reaches infinite velocity in a finite time is avoided. Furthermore, it allows us to obtain the coefficients of the Taylor expansion near the wall for boundary layers where the Helmholtz operator has been applied.
Related
- Boundary value problems for linear differential-algebraic equations: solvability via the Kronecker canonical form
- Nonlinear differential-algebraic systems with dissipative port-Hamiltonian structure
- Mathematical modeling, simulation and optimization via (port-Hamiltonian) differential-algebraic equations
- Boundary-layer asymptotics for Gaussian-smoothed singular measures
- An Algebraic Proof of the Non-Modularity of Solutions to the Canonical Modular Differential Equation
BibTeX
@misc{valencianegrete2026differential,
title = {{A Differential Algebraic Framework for Boundary Layer $α$-Models}},
author = {C. Valencia-Negrete and J. Flores and M. Perez and M. Romero de Terreros and M. Favela},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16442},
eprint = {2609.16442},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16442},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Differential Algebraic Framework for Boundary Layer α-Models
AU - C. Valencia-Negrete
AU - J. Flores
AU - M. Perez
AU - M. Romero de Terreros
AU - M. Favela
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16442
UR - https://arxiv.org/abs/2609.16442
AB - By addressing the problem of describing the differences between the saturation monoids of the Prandtl and Leray-α boundary layers, and algebraically distinguishing the action of the Helmholtz operator, we can show that, when the modification of the vector field is halted at a minimum scale determined by the differential filter, the paradox of constructing a solution that reaches infinite velocity in a finite time is avoided. Furthermore, it allows us to obtain the coefficients of the Taylor expansion near the wall for boundary layers where the Helmholtz operator has been applied.
ER -