Asymptotic equivalence and decay characterization in second-grade fluid equations

Felipe W. Cruz; César J. Niche; Cilon F. Perusato; Marko A. Rojas-Medar

doi:10.1016/j.jde.2026.114237

Asymptotic equivalence and decay characterization in second-grade fluid equations

Felipe W. Cruz
, César J. Niche
, Cilon F. Perusato
, Marko A. Rojas-Medar

Department of Mathematics

University of Seville
Universidade Federal de Pernambuco
Universidade Federal do Rio de Janeiro
Institut Camille Jordan

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

Abstract

We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the large-time behavior of these solutions by comparing them to the solutions of the linearized equations. As a consequence, we obtain lower bounds for the solutions. Other auxiliary results of interest are discussed.

Original language	English
Article number	114237
Journal	Journal of Differential Equations
Volume	463
DOIs	https://doi.org/10.1016/j.jde.2026.114237
State	Published - 15 May 2026

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10.1016/j.jde.2026.114237

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title = "Asymptotic equivalence and decay characterization in second-grade fluid equations",

abstract = "We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the large-time behavior of these solutions by comparing them to the solutions of the linearized equations. As a consequence, we obtain lower bounds for the solutions. Other auxiliary results of interest are discussed.",

author = "Cruz, \{Felipe W.\} and Niche, \{C{\'e}sar J.\} and Perusato, \{Cilon F.\} and Rojas-Medar, \{Marko A.\}",

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AU - Cruz, Felipe W.

AU - Niche, César J.

AU - Perusato, Cilon F.

AU - Rojas-Medar, Marko A.

PY - 2026/5/15

Y1 - 2026/5/15

N2 - We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the large-time behavior of these solutions by comparing them to the solutions of the linearized equations. As a consequence, we obtain lower bounds for the solutions. Other auxiliary results of interest are discussed.

AB - We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the large-time behavior of these solutions by comparing them to the solutions of the linearized equations. As a consequence, we obtain lower bounds for the solutions. Other auxiliary results of interest are discussed.

UR - https://www.scopus.com/pages/publications/105030259917

U2 - 10.1016/j.jde.2026.114237

DO - 10.1016/j.jde.2026.114237

M3 - Article

AN - SCOPUS:105030259917

SN - 0022-0396

VL - 463

JO - Journal of Differential Equations

JF - Journal of Differential Equations

M1 - 114237

ER -

Asymptotic equivalence and decay characterization in second-grade fluid equations

Abstract

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