$\CR$-Bounded Solution Operator for Navier-Stokes-Korteweg in Bent Half Space (Ω+)
Abstract
This paper discusses the $\CR$-bounded solution operator for a compressible fluid model of Korteweg type with slip boundary conditions in a bent half-space (Ω+). This result provides a foundation for studying the Navier-Stokes-Korteweg system in the Lp in time and Lq in space maximal regularity class and contributes to the analysis of local and global well-posedness for the original nonlinear problem, which is a fundamental system equation to describe the motion of the viscous fluid.
Full text article
References
J. E. Dunn and J. Serrin, “On the thermomechanics of interstitial working,” Arch. Rational Mech. Anal., vol. 88, no. 2, pp. 95–133, 1985. https://doi.org/10.1007/BF00250907.
D. M. Anderson, A. A. Wheeler, and G. B. McFadden, “Diffuse-interface methods in fluid mechanics,”
J. Liu, C. M. Landis, H. Gomez, and T. J. R. Hughes, “Liquid–vapor phase transition: Thermomechanical theory, entropy stable numerical formulation, and boiling simulations,” Computer Methods in Applied Mechanics and Engineering, vol. 297, no. 1, pp. 476–553, 2015. https://doi.org/10.1016/j.cma.2015.09.007.
D. Bresch, B. Desjardins, and C. K. Lin, “On some compressible fluid models: Korteweg, lubrication, and shallow water systems,” Comm. Partial Differ. Equ., vol. 28, no. 3–4, pp. 843–868, 2003. https://doi.org/10.1081/PDE-120020499.
M. Kotschote, “Strong solutions for a compressible fluid model of korteweg type,” Annales de l’Institut Henri Poincare´ C, Analyse non line´aire, vol. 25, no. 4, pp. 679–696, 2008. https://doi.org/10.1016/j.anihpc.2007.03.005.
M. Kotschote, “Strong well-posedness for a korteweg-type model for the dynamics of a compressible non-isothermal fluid,” J. Math. Fluid Mech., vol. 12, no. 4, pp. 473–484, 2010. https://doi.org/10.1007/s00021-009-0298-1.
H. Saito, “Compressible fluid model of korteweg type with free boundary condition: model problem,” Funkcial. Ekvac, vol. 62, no. 3, pp. 337–386, 2019. https://doi.org/10.1619/fesi.62.337.
H. Saito, “Existence of -bounded solution operator families for a compressible fluid model of korteweg type on the half-space,” Mathematical Methods in the Applied Sciences, vol. 44, no. 2, pp. 1744–1787, 2020. https://doi.org/10.1002/mma.6875.
S. Inna, S. Maryani, and H. Saito, “Half-space model problem for a compressible fluid model of korteweg type with slip boundary condition,” in Journal of Physics: Conference Series, vol. 1494, pp. 1–11, IOP Publishing Ltd, 2020. https://doi.org/10.1088/1742-6596/1494/1/012014.
S. Inna, I. Fauziah, M. Manaqib, and P. M. Puri, “Operator solusi model fluida termampatkan tipe korteweg dengan kondisi batas slip di half-space kasus koefisien ((μ + ν)/(2κ))2 − (1/κ)̸ = 0, dengan κ = μν dan μ̸ = ν,” Limits: Journal of Mathematics and its Applications, vol. 20, no. 2, pp. 191–208, 2023. http://dx.doi.org/10.12962/limits.v20i2.12954.
S. Inna, “The existence of r-bounded solution operator of navier stokes korteweg model with slip boundary conditions in half-space,” Math. Meth. Appl. Sci., vol. 47, no. 11, pp. 8581–8610, 2024. https://doi.org/10.1002/mma.10033.
S. Inna and H. Saito, “Local solvability for a compressible fluid model of korteweg type on general domains,” Mathematics, vol. 11, no. 2368, pp. 1–41, 2023. https://doi.org/10.3390/math11102368.
H. Saito, “On the maximal lp-lq regularity for a compressible fluid model of korteweg type on general domains,” Journal of Differential Equations, vol. 268, no. 6, pp. 2802–2851, 2020. https://doi.org/10.1016/j.jde.2019.09.040.
V. Lebedev, An Introduction to Functional Analysis in Computational Mathematics. Birkhauser, Boston, 1997. https://doi.org/10.1007/978-1-4612-4128-7.
Authors
Copyright (c) 2025 Journal of the Indonesian Mathematical Society
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Article Details
