Global well-posedness for second grade fluids

H. R. Clark; L. Friz; M. Rojas-Medar

doi:10.1142/S0219530524300011

Global well-posedness for second grade fluids

H. R. Clark
, L. Friz
, M. Rojas-Medar

Universidade Federal do Delta do Parnaíba
Universidad del Bío-Bío
University of Taparacá

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This paper deals with a study on an initial-boundary value problem for incompressible non-Newtonian fluids of degree two, in a bounded and simply connected open set Ω of R3. It will be shown that the global-in-time weak solution is uniformly stable (i.e. the behavior of the solution changes continuously with the data), and consequently this solution is unique. Furthermore, an exponential decay rate for the energy of the weak solution will also be established.

Original language	English
Pages (from-to)	169-192
Number of pages	24
Journal	Analysis and Applications
Volume	23
Issue number	2
DOIs	https://doi.org/10.1142/S0219530524300011
State	Published - 1 Feb 2025
Externally published	Yes

Keywords

Second grade fluid equation
energy exponential decay
uniform stability of the solution
uniqueness of the solution

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10.1142/S0219530524300011

Cite this

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N2 - This paper deals with a study on an initial-boundary value problem for incompressible non-Newtonian fluids of degree two, in a bounded and simply connected open set Ω of R3. It will be shown that the global-in-time weak solution is uniformly stable (i.e. the behavior of the solution changes continuously with the data), and consequently this solution is unique. Furthermore, an exponential decay rate for the energy of the weak solution will also be established.

AB - This paper deals with a study on an initial-boundary value problem for incompressible non-Newtonian fluids of degree two, in a bounded and simply connected open set Ω of R3. It will be shown that the global-in-time weak solution is uniformly stable (i.e. the behavior of the solution changes continuously with the data), and consequently this solution is unique. Furthermore, an exponential decay rate for the energy of the weak solution will also be established.

KW - Second grade fluid equation

KW - energy exponential decay

KW - uniform stability of the solution

KW - uniqueness of the solution

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Global well-posedness for second grade fluids

Abstract

Keywords

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