Weak-strong uniqueness for the compressible fluid-rigid body interaction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00521522" target="_blank" >RIV/67985840:_____/20:00521522 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jde.2019.10.038" target="_blank" >https://doi.org/10.1016/j.jde.2019.10.038</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2019.10.038" target="_blank" >10.1016/j.jde.2019.10.038</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Weak-strong uniqueness for the compressible fluid-rigid body interaction

Popis výsledku v původním jazyce

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position and velocity of the rigid body in the fluid are unknown and the motion of the rigid body is driven by the normal stress forces of the fluid acting on the boundary of the body. We prove that the strong solution, which is known to exist under certain smallness assumptions, is unique in the class of weak solutions to the problem. The proof relies on a correct definition of the relative energy, to use this tool we then have to introduce a change of coordinates to transform the strong solution to the domain of the weak solution in order to use it as a test function in the relative energy inequality. Estimating all arising terms we prove that the weak solution has to coincide with the transformed strong solution and finally that the transformation has to be in fact an identity.

Název v anglickém jazyce

Weak-strong uniqueness for the compressible fluid-rigid body interaction

Popis výsledku anglicky

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position and velocity of the rigid body in the fluid are unknown and the motion of the rigid body is driven by the normal stress forces of the fluid acting on the boundary of the body. We prove that the strong solution, which is known to exist under certain smallness assumptions, is unique in the class of weak solutions to the problem. The proof relies on a correct definition of the relative energy, to use this tool we then have to introduce a change of coordinates to transform the strong solution to the domain of the weak solution in order to use it as a test function in the relative energy inequality. Estimating all arising terms we prove that the weak solution has to coincide with the transformed strong solution and finally that the transformation has to be in fact an identity.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-04243S" target="_blank" >GA19-04243S: Parciální diferenciální rovnice v mechanice a termodynamice tekutin</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Svazek periodika

268

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

4756-4785

Kód UT WoS článku

000510863100023

EID výsledku v databázi Scopus

2-s2.0-85075398778