On the characterization of the Navier-Stokes flows with the power-like energy decay
Result 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.
Keywords
Navier–Stokes equationslarge-time energy decayhomogeneous Besov space
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
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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Classification
Type
Jimp - 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)
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Fluid Mechanics
ISSN
1422-6928
e-ISSN
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Volume of the periodical
16
Issue of the periodical within the volume
3
Country of publishing house
CH - SWITZERLAND
Number of pages
15
Pages from-to
431-446
UT code for WoS article
000340559700002
EID of the result in the Scopus database
2-s2.0-84906836866
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Fluids and plasma physics (including surface physics)
Year of implementation
2014