A Priori Estimates for a System Modelling Nonhomogeneous Asymmetric Fluids

Abstract

In this article, we prove some a priori estimates for a system of partial differential equations arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The unknowns of the system are the velocity field of the fluid particles, the angular velocity of rotation of the fluid particles, the mass density of the fluid and the pressure distribution. For the density functions we consider the application of the Helmholtz decomposition.

Keywords:

• A priori estimates
• micropolar fluids
• Navier-Stokes system
• nonhomogeneous asymmetric fluids

MATHEMATICS SUBJECT CLASSIFICATION:

• 92D30
• 92D25
• 49K20
• 49N45

Authors’ contributions

All authors contributed equally to the writing of this article. All authors read and approved the final manuscript.

Disclosure Statement

The authors declare that they have no competing interests.

Additional information

Funding

AC thanks the partial support of Universidad del Bío-Bío (Chile) through the research projects: 2120436 IF/R, research project INES I+D 22-14; and FAPEI; and Universidad Tecnol\’ogica Metropolitana (Chile) through the project supported by the Competition for Research Regular Projects, year 2020, Code LPR20-06. EF-C thanks the partial support of MICINN (Spain) through Grant MTM2016-76990-P. MR-M thanks the partial support of MATH-AMSUD project, MATH-03 (CTMicrAAPDEs), and CAPES-PRINT 88887.311962/2018-00 (Brazil). EF-C and MR-M were partially supported by ANID/PCI/MEC-Atraccióon de Capital Humano Avanzado del Extranjero No. 80170081 (Chile). AT thanks support of CONICYT (Chile) through the program “Becas de Doctorado”.