Exponent bounds for a convolution inequality in Euclidean space with applications to the Navier-Stokes equations
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- by Chris Orum and Mina Ossiander PDF
- Proc. Amer. Math. Soc. 141 (2013), 3883-3897 Request permission
Abstract:
The convolution inequality $h*h(\xi ) \leq B |\xi |^\theta h(\xi )$ defined on $\mathbf {R}^n$ arises from a probabilistic representation of solutions of the $n$-dimensional Navier-Stokes equations, $n \geq 2$. Using a chaining argument, we establish in all dimensions $n \geq 1$ the nonexistence of strictly positive fully supported solutions of this inequality for $\theta \geq n/2.$ We use this result to describe a chain of continuous embeddings from spaces associated with probabilistic solutions to the spaces $BMO^{-1}$ and $BMO_T^{-1}$ associated with the Koch-Tataru solutions of the Navier-Stokes equations.References
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Additional Information
- Chris Orum
- Affiliation: Department of Mathematics, University of Utah, 155 S. 1400 E., Room 233, Salt Lake City, Utah 84112-0090
- Address at time of publication: Mathematics Program, Eastern Oregon University, La Grande, Oregon 97850
- Email: orum@math.utah.edu, orum@math.utah.edu
- Mina Ossiander
- Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605
- Email: ossiand@math.oregonstate.edu
- Received by editor(s): January 13, 2011
- Received by editor(s) in revised form: January 22, 2012
- Published electronically: July 30, 2013
- Additional Notes: This work was partially supported by the U.S. National Science Foundation through the Focussed Research Group collaborative awards DMS-0073958 and DMS-0940249
- Communicated by: Walter Craig
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3883-3897
- MSC (2010): Primary 35Q30, 76D05, 42B37; Secondary 76M35, 39B72, 60J80
- DOI: https://doi.org/10.1090/S0002-9939-2013-11662-X
- MathSciNet review: 3091777