Weak solutions for Euler systems with non-local interactions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00475228" target="_blank" >RIV/67985840:_____/17:00475228 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1112/jlms.12027" target="_blank" >http://dx.doi.org/10.1112/jlms.12027</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.12027" target="_blank" >10.1112/jlms.12027</a>

Result language
angličtina
Original language name
Weak solutions for Euler systems with non-local interactions
Original language description
We consider several modifications of the Euler system of fluid dynamics, including its pressureless variant driven by non-local interaction repulsive–attractive and alignment forces in the space dimension N=2,3. These models arise in the study of self-organization in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of infinitely many global-in-time weak solutions for any bounded initial data. Then we consider the class of dissipative solutions satisfying, in addition, the associated global energy balance (inequality). We identify a large set of initial data for which the problem admits infinitely many dissipative weak solutions. Finally, we establish a weak–strong uniqueness principle for the pressure-driven Euler system with non-local interaction terms as well as for the pressureless system with Newtonian interaction.
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
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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