Optimal initial condition for the local existence of strong solutions of the micropolar fluids

Miguel Loayza; Marcos Rocha-Silva; Marko Rojas-Medar

doi:10.1142/S0219530526500399

Optimal initial condition for the local existence of strong solutions of the micropolar fluids

Miguel Loayza
, Marcos Rocha-Silva
, Marko Rojas-Medar

Department of Mathematics

Universidade Federal de Pernambuco

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

Abstract

In this paper, we study the micropolar fluid system in a bounded three-dimensional domain and establish a necessary and sufficient condition on the initial data for the existence of a local strong solution. Our approach is based on the theory of weak solutions, which relies essentially on rewriting the problem in integral form and applying a fixed point argument. In addition, we investigate the uniqueness of weak solutions in the class L^s(0, T; L^q(Ω)) satisfying the condition 2/s + 3/q = 1.

Original language	English
Journal	Analysis and Applications
DOIs	https://doi.org/10.1142/S0219530526500399
State	Accepted/In press - 2026

Keywords

local in time regularity
Micropolar fluids
Serrin’s class
weak and strong solutions

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10.1142/S0219530526500399

Cite this

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abstract = "In this paper, we study the micropolar fluid system in a bounded three-dimensional domain and establish a necessary and sufficient condition on the initial data for the existence of a local strong solution. Our approach is based on the theory of weak solutions, which relies essentially on rewriting the problem in integral form and applying a fixed point argument. In addition, we investigate the uniqueness of weak solutions in the class Ls(0, T; Lq(Ω)) satisfying the condition 2/s + 3/q = 1.",

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T1 - Optimal initial condition for the local existence of strong solutions of the micropolar fluids

AU - Loayza, Miguel

AU - Rocha-Silva, Marcos

AU - Rojas-Medar, Marko

PY - 2026

Y1 - 2026

N2 - In this paper, we study the micropolar fluid system in a bounded three-dimensional domain and establish a necessary and sufficient condition on the initial data for the existence of a local strong solution. Our approach is based on the theory of weak solutions, which relies essentially on rewriting the problem in integral form and applying a fixed point argument. In addition, we investigate the uniqueness of weak solutions in the class Ls(0, T; Lq(Ω)) satisfying the condition 2/s + 3/q = 1.

AB - In this paper, we study the micropolar fluid system in a bounded three-dimensional domain and establish a necessary and sufficient condition on the initial data for the existence of a local strong solution. Our approach is based on the theory of weak solutions, which relies essentially on rewriting the problem in integral form and applying a fixed point argument. In addition, we investigate the uniqueness of weak solutions in the class Ls(0, T; Lq(Ω)) satisfying the condition 2/s + 3/q = 1.

KW - local in time regularity

KW - Micropolar fluids

KW - Serrin’s class

KW - weak and strong solutions

UR - https://www.scopus.com/pages/publications/105033650201

U2 - 10.1142/S0219530526500399

DO - 10.1142/S0219530526500399

M3 - Article

AN - SCOPUS:105033650201

SN - 0219-5305

JO - Analysis and Applications

JF - Analysis and Applications

ER -

Optimal initial condition for the local existence of strong solutions of the micropolar fluids

Abstract

Keywords

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