Fast Decaying Solutions of the Navier-Stokes Equation and Asymptotic Properties |
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Authors: | Bruno Scarpellini |
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Institution: | (1) Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland |
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Abstract: | While the basic global existence problem for the Navier-Stokes
equations seems to remain open, there are related questions of
some interest which are amenable to discussion: find large
initial data giving rise to global solutions. Such initial data
are known in the literature. A study shows that they have a
peculiar property: they give rise to solutions which decay fast
in very short time. A major result to be proved states that the
set of trajectories induced by such initial data is dense in
every open set (with respect to some fractional power norm). A
further result states that if the exterior force f is zero,
then such rapid decays cannot occur infinitely often along
trajectories. This follows from some inequalities, connecting
and
, with A the Stokes operator. |
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Keywords: | 35Q30 76D05 76N10 |
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