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Axioms 2013, 2(2), 100-121; doi:10.3390/axioms2020100

Divergence-Free Multiwavelets on the Half Plane

1,*  and 2
1 Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA 2 Hanoi Institute of Mathematics, 18 Hoang Quoc Viet, Hanoi, Vietnam
* Author to whom correspondence should be addressed.
Received: 24 December 2012 / Revised: 16 March 2013 / Accepted: 18 March 2013 / Published: 11 April 2013
(This article belongs to the Special Issue Wavelets and Applications)
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We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R2 + such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R2 +. Such wavelets are suitable to study the Navier–Stokes equations on a half plane when imposing a Navier boundary condition.
Keywords: multiwavelets; divergence-free wavelets; fractal interpolation function multiwavelets; divergence-free wavelets; fractal interpolation function
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Lakey, J.; Nguyen, P. Divergence-Free Multiwavelets on the Half Plane. Axioms 2013, 2, 100-121.

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