Navier-Stokes equations on a flat cylinder with vorticity production on the boundary

We study a singular version of the incompressible two-dimensional Navier-Stokes (NS) system on a flat cylinder C, with Neumann conditions for the vorticity and a vorticity production term on the boundary [partialdifferential]C to restore the no-slip boundary condition for the velocity u sub(|[partia...

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Bibliographic Details
Published in:Nonlinearity 2011-09, Vol.24 (9), p.2639-2662
Main Authors: BOLDRIGHINI, Carlo, BUTTA, Paolo
Format: Article
Language:English
Subjects:
Boundaries
Cylinders
Differential equations
Exact sciences and technology
Flats
Global analysis, analysis on manifolds
Mathematical analysis
Mathematical methods in physics
Mathematics
Navier-Stokes equations
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Other topics in mathematical methods in physics
Partial differential equations
Physics
Restoration
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Vorticity
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Summary:We study a singular version of the incompressible two-dimensional Navier-Stokes (NS) system on a flat cylinder C, with Neumann conditions for the vorticity and a vorticity production term on the boundary [partialdifferential]C to restore the no-slip boundary condition for the velocity u sub(|[partialdifferential])C= 0. The problem is formulated as an infinite system of coupled ordinary differential equations (ODEs) for the Neumann Fourier modes. For a general class of initial data we prove existence and uniqueness of the solution, and equivalence to the usual NS system. The main tool in the proofs is a suitable decay of the modes, obtained by the explicit form of the ODEs. We finally show that the resulting expansions of the velocity u and of its first and second space derivatives converge and define continuous functions up to the boundary.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/24/9/014