A dyadic shell model of the 3D Navier-Stokes equations exhibits finite-time blow-up from smooth initial data and forcing, with singularity formation also shown in the inviscid unforced case just above the energy level.
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2026 2verdicts
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The large-time asymptotics of 2D micropolar flows depend only on kinematic viscosity μ, independent of χ, γ, and κ, via a new enstrophy-like identity relating fluid vorticity to micro-angular velocity.
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Finite-time blow-up in an elementary model of the 3D Navier-Stokes equations
A dyadic shell model of the 3D Navier-Stokes equations exhibits finite-time blow-up from smooth initial data and forcing, with singularity formation also shown in the inviscid unforced case just above the energy level.
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On the Role of the Viscosity Parameters in the Large Time Asymptotics of 2D Micropolar Flows
The large-time asymptotics of 2D micropolar flows depend only on kinematic viscosity μ, independent of χ, γ, and κ, via a new enstrophy-like identity relating fluid vorticity to micro-angular velocity.