A note on weak solutions of conservation laws and energy/entropy conservation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00490764" target="_blank" >RIV/67985840:_____/18:00490764 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00205-018-1238-0" target="_blank" >http://dx.doi.org/10.1007/s00205-018-1238-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00205-018-1238-0" target="_blank" >10.1007/s00205-018-1238-0</a>
Alternative languages
Result language
angličtina
Original language name
A note on weak solutions of conservation laws and energy/entropy conservation
Original language description
A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such cases most often related to the second law of thermodynamics. This observation easily generalizes to any symmetrizable system of conservation laws, they are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake the role of physical admissibility conditions for weak solutions. We want to answer the question: what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality? An archetypal example of such a result was derived for the incompressible Euler system in the context of Onsager’s conjecture in the early nineties. This general result can serve as a simple criterion to numerous systems of mathematical physics to prescribe the regularity of solutions needed for an appropriate companion law to be satisfied.
Czech name
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Czech description
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Classification
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
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
e-ISSN
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Volume of the periodical
229
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
16
Pages from-to
1223-1238
UT code for WoS article
000435367300008
EID of the result in the Scopus database
2-s2.0-85044357804