A note on weak solutions of conservation laws and energy/entropy conservation
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
A note on weak solutions of conservation laws and energy/entropy conservation
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
A note on weak solutions of conservation laws and energy/entropy conservation
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2018
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
e-ISSN
—
Svazek periodika
229
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
DE - Spolková republika Německo
Počet stran výsledku
16
Strana od-do
1223-1238
Kód UT WoS článku
000435367300008
EID výsledku v databázi Scopus
2-s2.0-85044357804