Strong solutions for two-dimensional nonlocal Cahn?Hilliard?Navier?Stokes systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F13%3A00394922" target="_blank" >RIV/67985840:_____/13:00394922 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jde.2013.07.016" target="_blank" >http://dx.doi.org/10.1016/j.jde.2013.07.016</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2013.07.016" target="_blank" >10.1016/j.jde.2013.07.016</a>
Alternative languages
Result language
angličtina
Original language name
Strong solutions for two-dimensional nonlocal Cahn?Hilliard?Navier?Stokes systems
Original language description
A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard Cahn-Hilliard equation has been replaced by its nonlocal version. The only known results are essentially the existence of a global weak solution and the existence of a suitable notion of global attractor for the corresponding dynamical system defined without uniqueness.In fact,even in the two-dimensional case, uniqueness of weak solutions is still an open problem. Here we take a step forward in the case of regular potentials. First we prove the existence of a (unique) strong solution in two dimensions. Then we show that any weak solution regularizes in finite time uniformly with respect to bounded sets of initial data. This result allows us to deduce that the global attractor is the union of all the bounded complete trajectories which are strong solutions.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP201%2F10%2F2315" target="_blank" >GAP201/10/2315: Mathematical modeling of Processes in Hysteretic Materials</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
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 Differential Equations
ISSN
0022-0396
e-ISSN
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Volume of the periodical
255
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
28
Pages from-to
2587-2614
UT code for WoS article
000323584900002
EID of the result in the Scopus database
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