粘弹性相分离模型在二维空间中强解的整体存在性
The Overall Existence of Strong Solution for Viscoelastic Phase Separation Model in the Two Dimensional Space
摘要: 本文给出了粘弹性相分离模型在二维空间下强解的整体存在性，使用Gagliardo-Nirenberg不等式、Sobolev不等式和Gronwall不等式进行证明，还使用了先验估计的证明方法。
Abstract: We present the overall existence of strong solutions for the viscoelastic phase separation model in two dimensions, using Gagliardo-Nirenberg inequality, Sobolev inequality and Gronwall inequality, and also the proof method of prior estimation.
文章引用：裴小田. 粘弹性相分离模型在二维空间中强解的整体存在性[J]. 应用数学进展, 2023, 12(6): 2749-2757. https://doi.org/10.12677/AAM.2023.126275

参考文献

[1] Brunk, A. and Lukacova-Medvidova, M. (2022) Global Existence of Weak Solutions to Viscoelastic Phase Separation: Part I Regular Case. arXiv:1907.03480v3.
[2] Lukacova-Medvidova, M., Mizerova, H. and Necasova, S. (2015) Global Existence and Uniqueness Result for the Diffusive Peterlin Viscoelastic Model. Nonlinear Analysis: Theory, Methods & Applications, 120, 154-170. [Google Scholar] [CrossRef] 
[3] Strasser, P.J., Tierra, G., Dunweg, B. and Lukacova-Medvidova, M. (2019) Energy-Stable Linearschemes for Polymer-Solvent Phase Field Models. Computers & Mathematics with Applica-tions, 77, 125-143.
[4] Zhou, D., Zhang, P.W. and E, W.N. (2006) Modified Models of Polymer Phase Separation. Physical Review E, 73, Article ID: 061801. [Google Scholar] [CrossRef] 
[5] Chupin, L. (2003) Existence Result for a Mixture of Non Newtonian Flows with Stress Diffusion Using the Cahn- Hilliard Formulation. Discrete and Continuous Dynamical Systems-B, 3, 45-68. [Google Scholar] [CrossRef] 
[6] Abels, H. (2009) On a Diffuse Interface Model for Two-Phase Flows of Viscous, Incompressible Fluids with Matched Densities. Archive for Rational Mechanics and Analysis, 194, 463-506. [Google Scholar] [CrossRef] 
[7] Abels, H., Depner, D. and Garcke, H. (2013) On an Incompressi-ble Navier-Stokes/Cahn-Hilliard System with Degenerate Mobility. Annales de l’Institut Henri Poincaré Analyse Nom Linéaire, 30, 1175-1190. [Google Scholar] [CrossRef] 
[8] Spiller, D., Brunk, A., Habrich, O., Egger, H., Lukaco-va-Medvidova, M. and Dunweg, B. (2021) Systematic Derivation of Hydrodynamic Equations for Viscoelastic Phase Separation. Journal of Physics: Condensed Matter, 33, Article ID: 364001. [Google Scholar] [CrossRef] 
[9] Tanaka, H. (2000) Viscoelastic Phase Separation. Journal of Physics: Condensed Matter, 12, R207. [Google Scholar] [CrossRef] 
[10] Lukacova-Medvidova, M., Mizerova, H., Notsu, H. and Tabata, M. (2017) Numerical Analysis of the Oseen-Type Peterlin Viscoelastic Model by the Stabilized Lagrange-Galerkin Method. Part II: A Linear Scheme. ESAIM: M2AN, 51, 1663-1689. [Google Scholar] [CrossRef] 

为你推荐