Analysis of the linear navier stokes korteweg model with neumann boundary conditions in three dimensional half-space
DOI:
https://doi.org/10.30606/absis.v7i1.2589Keywords:
Neumann, Transformasi Fourier Parsial, extensions, navier stokes korteweg, resolvent equation, partial fourier transformation, persamaan resolventAbstract
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.
Downloads
References
Desjardins, B., & Danchin, R. (2001). Existence of solutions for compressible fluid models of Korteweg type. Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 18(1), 97-133. https://doi.org/10.1016/S0294-1449(00)00056-1
Dunn, J., & Serrin, J. (1985). On the thermomechanics of interstitial working. Archive for Rational Mechanics and Analysis, 88(2), 95-133. https://api.semanticscholar.org/CorpusID:121445779
Haspot, B. (2011). Existence of global weak solution for compressible fluid models of Korteweg type. Journal of Mathematical Fluid Mechanics, 13(2), 223-249. https://doi.org/10.1007/s00021-009-0013-2
Hattori, H., & Li, D. (1996). Global solutions of a high dimensional system for Korteweg materials. Journal of Mathematical Analysis and Applications, 198(1), 84-97.
Inna, S. (2024). The existence of R-bounded solution operator for Navier-Stokes Korteweg model with slip boundary conditions in half-space. Mathematical Methods in the Applied Sciences. In Press.
Inna, S., & Saito, H. (2023). Local solvability for a compressible fluid model of Korteweg type on general domains. Mathematics, 11(10), 2368. https://doi.org/10.3390/math11102368
Inna, S., Fauziah, I., Manaqib, M., & Putri, P. M. (2023). Operator solusi model fluida termampatkan tipe Korteweg dengan kondisi batas slip di half-space kasus koefisien (μ+ν)/(2κ))2−(1/κ)>0(mu + nu)/(2 kappa))^2 -(1/kappa) > 0(μ+ν)/(2κ))2−(1/κ)>0, κ=μνkappa = mu nuκ=μν, μ≠νmu neq nuμ=ν. LIMITS, 20(2), 191-203. https://doi.org/10.12962/limits.v20i2.12954
Inna, S., Maryani, S., & Saito, H. (2020). Half-space model problem for a compressible fluid model of Korteweg type with slip boundary condition. Journal of Physics: Conference Series, 1494, 012014. https://doi.org/10.1088/1742-6596/1494/1/012014
Kotschote, M. (2008). Strong solutions for a compressible fluid model of Korteweg type. Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 25(4), 679-696. https://doi.org/10.1016/j.anihpc.2007.03.005
Prayugo, J., Inna, S., Mahmudi, & Damiati, N. (2024). Solusi model linear Navier-Stokes-Korteweg di R+3R_+^3R+3 dengan syarat batas slip. Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika, 5(1), 262-277. https://doi.org/10.46306/lb.v5i1.554
Pritchard, P. J. (2011). Introduction to fluid mechanics (8th ed.). Wiley.
Ridwan. (1999). Seri diktat kuliah mekanika fluida dasar. Gunadarma.
Saito, H. (2019). Compressible fluid model of Korteweg type with free boundary condition: Model problem. Funkcialaj Ekvacioj, 62(3), 337-386. https://doi.org/10.1619/fesi.62.337
Saito, H. (2020). Existence of R-bounded solution operator families for a compressible fluid model of Korteweg type on the half-space. Mathematical Methods in the Applied Sciences, 44(2), 1744-1787. https://arxiv.org/abs/1901.06461
Salsabila, A., Inna, S., Liebenlito, M., & Purnomowati, R. (2024). Solusi model Navier-Stokes Korteweg dengan syarat batas slip di half-space berdimensi 3. Jurnal Matematika dan Pendidikan Matematika, 7(1), 1-15. https://doi.org/10.36815/majamath.v7i1.3158.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Dwi Windari Nur Khasanah, Suma Inna, Madona Yunita Wijaya, Sri Indriati Hasanah
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
