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Khasanah, Dwi Windari Nur
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Mathematics

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Analysis of the linear navier stokes korteweg model with neumann boundary conditions in three dimensional half-space Khasanah, Dwi Windari Nur; Inna, Suma; Wijaya, Madona Yunita; Hasanah, Sri Indriati
Jurnal Absis: Jurnal Pendidikan Matematika dan Matematika Vol. 7 No. 1 (2024): Jurnal Absis
Publisher : Program Studi Pendidikan Matematika Universitas Pasir Pengaraian

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30606/absis.v7i1.2589

Abstract

This study discusses the solution of the Navier-Stokes Korteweg model, which describes two-phase fluid flow with capillary effects, with Neumann boundary conditions in the half-space. The main objective is to detail the resolution process of the resolvent equation system in the half-space related to the Navier-Stokes Korteweg model with Neumann boundary conditions. The resolution is carried out in several steps. First, the resolvent equation system is reduced using even and odd extensions. Then, a partial Fourier transform is applied, resulting in a simpler ordinary differential equation. The findings of this research indicate the existence of a solution operator for the resolvent equation of the Navier-Stokes Korteweg model with Neumann boundary conditions in the half-space. This solution applies for two cases involving the coefficients, depending on certain conditions related to the fluid properties.
Analysis of the linear navier stokes korteweg model with neumann boundary conditions in three dimensional half-space Khasanah, Dwi Windari Nur; Inna, Suma; Wijaya, Madona Yunita; Hasanah, Sri Indriati
Jurnal Absis: Jurnal Pendidikan Matematika dan Matematika Vol. 7 No. 1 (2024): Jurnal Absis
Publisher : Program Studi Pendidikan Matematika Universitas Pasir Pengaraian

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30606/absis.v7i1.2589

Abstract

This study discusses the solution of the Navier-Stokes Korteweg model, which describes two-phase fluid flow with capillary effects, with Neumann boundary conditions in the half-space. The main objective is to detail the resolution process of the resolvent equation system in the half-space related to the Navier-Stokes Korteweg model with Neumann boundary conditions. The resolution is carried out in several steps. First, the resolvent equation system is reduced using even and odd extensions. Then, a partial Fourier transform is applied, resulting in a simpler ordinary differential equation. The findings of this research indicate the existence of a solution operator for the resolvent equation of the Navier-Stokes Korteweg model with Neumann boundary conditions in the half-space. This solution applies for two cases involving the coefficients, depending on certain conditions related to the fluid properties.
Co-Authors Hasanah, Sri Indriati Inna, Suma Wijaya, Madona Yunita