On Local Two-Point Strain Coercivity in the 3D Vorticity Equation
Year: 2026
Type: preprint
Abstract: Short self-contained note on a conjectured local two-point strain coercivity inequality for the 3D incompressible Navier–Stokes vorticity equation on T^3. Shows (Theorem A) that Conjecture (*)_rho fails as a kinematic identity for general smooth divergence-free fields on T^3 via intermediate-axis alignment with a slow spatial tilt toward the principal stretching direction, and (Theorem B) that after Biot–Savart and absorption without a priori Lipschitz control of the vorticity direction field xi = omega/|omega|, the resulting bound has leading coefficient C_* = C_CZ * M rather than a negative damping constant -gamma. Also shows that a global two-point coercivity bound without a short-range cutoff |x-y| <= rho fails on exact stationary 2D Navier–Stokes shear flows.
Author: Frohman, Benjamin Stanley
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223443202