On the characterization of the Navier-Stokes flows with the power-like energy decay

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985874%3A_____%2F14%3A00431421" target="_blank" >RIV/67985874:_____/14:00431421 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00021-014-0164-7" target="_blank" >http://dx.doi.org/10.1007/s00021-014-0164-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00021-014-0164-7" target="_blank" >10.1007/s00021-014-0164-7</a>

Result language
angličtina
Original language name
On the characterization of the Navier-Stokes flows with the power-like energy decay
Original language description
We study the energy decay of the turbulent solutions to the Navier-Stokes equations in the whole three-dimensional space. We show as the main result that the solutions with the energy decreasing at the rate O(t−α),t→∞, α in [0,5/2] , are exactly characterized by their initial conditions belonging into the homogeneous Besov space dotB− α2,∞ . Similarly, for a solution u and p in [1,∞] the integral int∞0|t α/2u(t)|p1/t dt is finite if and only if the initial condition of u belongs to the homogeneous Besov space dotB− α2,p . For the case α in (5/2,9/2] we present analogical results for some subclasses of turbulent solutions.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10305 - Fluids and plasma physics (including surface physics)

Project
<a href="/en/project/GA14-02067S" target="_blank" >GA14-02067S: Advanced methods for flow-field analysis</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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