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Exponent bounds for a convolution inequality in Euclidean space with applications to the Navier-Stokes equations by Orum, Chris; Ossiander, Mina is a scholarly article available to read on EtoBox.

What is Exponent bounds for a convolution inequality in Euclidean space with applications to the Navier-Stokes equations about?

The convolution inequality $h*h(\xi) \leq B |\xi|^\theta h(\xi)$ defined on $\Rn$ arises from a probabilistic representation of solutions of the $n$-dimensional Navier-Stokes equations, $n \geq 2$. Using a chaining argument, we establish the nonexistence of strictly positive fully supported solutions of this inequality if $\theta \geq n/2$, in all dimensions $n \geq 1$. 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.

Author

Orum, Chris; Ossiander, Mina

Published

2012

Language

EN