Pile-up flow-solutions toNavier-Stokes equations in the Millennium Prize Problem-version with isochoric condition and regularity requirements

Volume 1, Issue 1, October 2016     |     PP. 145-148      |     PDF (182 K)    |     Pub. Date: November 19, 2016
DOI:    420 Downloads     5455 Views  

Author(s)

Lena J-T Strömberg, Previously Dep of Solid Mechanics, Royal Inst of Technology, KTH

Abstract
Solutions to the Navier-Stokes equations for the Millenium Prize Problem are provided. These consist of a transient Pile-Up flow. A proof is given to show that the flow functions satisfy the Boundary Conditions at infinity. The proof for the spatial derivatives of velocity, u, and force, f, relies on decomposition of an exponential function, Cauchy-Schwarz and induction.

Keywords
Navier-Stokes, Millennium Prize, Pile Up flow, Lena Pile-Up, Theorem, Proof, decomposition, Cauchy-Schwarz, induction, exponential function, velocity, coordinates

Cite this paper
Lena J-T Strömberg, Pile-up flow-solutions toNavier-Stokes equations in the Millennium Prize Problem-version with isochoric condition and regularity requirements , SCIREA Journal of Mathematics. Volume 1, Issue 1, October 2016 | PP. 145-148.

References

[ 1 ] Charles Fefferman. (2000) http://en.wikipedia.org/wiki/NavierStokes_existence_and_smoothness http://www.claymath.org/millennium/Navier-Stokes_Equations/
[ 2 ] Strömberg L (2007). Formations of matter, light and sound described with Bernoulli's principle 10th ESAFORM Conference on Material Forming, Pts A and B / [ed] Cueto, E; Chinesta, F, MELVILLE: AMER INST PHYSICS, Vol. 907, 53-58 s.
[ 3 ] Strömberg L (2016). Noncircular orbits at MC vehicle wobbling, in whirls and for light, LAP Lambert Academic publishing, Germany. ISBN-13 978-3-659-85664-8.