Rigorous Derivation of a 1D Model from the 3D Non-Steady Navier-Stokes Equations for Compressible Nonlinearity Viscous Fluids

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73589084" target="_blank" >RIV/61989592:15310/18:73589084 - isvavai.cz</a>

Výsledek na webu

<a href="https://ejde.math.txstate.edu/Volumes/2018/114/andrasik.pdf" target="_blank" >https://ejde.math.txstate.edu/Volumes/2018/114/andrasik.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Rigorous Derivation of a 1D Model from the 3D Non-Steady Navier-Stokes Equations for Compressible Nonlinearity Viscous Fluids

Popis výsledku v původním jazyce

Problems with three-dimensional models lie very often in their large complexity leading to impossibility to find an analytical solution. Numerical solutions are sometimes an option, but they can be unduly complicated in the case of three-dimensional models. Frequently, researchers investigate models where one or even two dimensions are almost negligible and nothing important is occurring in them. These models can be simplified and turned into one- or two-dimensional models, which is very helpful, because their solutions are easier than solutions of the original three-dimensional models. Since nonsteady Navier-Stokes equations for compressible nonlinearly viscous fluids in a three-dimensional domain belongs to the class of models which need a simplification, when possible, to be eifectively solved, we performed a dimension reduction for this model. We studied the dynamics of a compressible fluid in thin domains where only one dimension is dominant. We present a rigorous derivation of a one-dimensional model from the three-dimensional Navier-Stokes equations.

Název v anglickém jazyce

Rigorous Derivation of a 1D Model from the 3D Non-Steady Navier-Stokes Equations for Compressible Nonlinearity Viscous Fluids

Popis výsledku anglicky

Problems with three-dimensional models lie very often in their large complexity leading to impossibility to find an analytical solution. Numerical solutions are sometimes an option, but they can be unduly complicated in the case of three-dimensional models. Frequently, researchers investigate models where one or even two dimensions are almost negligible and nothing important is occurring in them. These models can be simplified and turned into one- or two-dimensional models, which is very helpful, because their solutions are easier than solutions of the original three-dimensional models. Since nonsteady Navier-Stokes equations for compressible nonlinearly viscous fluids in a three-dimensional domain belongs to the class of models which need a simplification, when possible, to be eifectively solved, we performed a dimension reduction for this model. We studied the dynamics of a compressible fluid in thin domains where only one dimension is dominant. We present a rigorous derivation of a one-dimensional model from the three-dimensional Navier-Stokes equations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Differential Equations

ISSN

1072-6691

e-ISSN

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Svazek periodika

2018

Číslo periodika v rámci svazku

MAY

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

"114-1"-"114-21"

Kód UT WoS článku

000432745500001

EID výsledku v databázi Scopus

2-s2.0-85047163565