一类化学活性流体方程组解的存在唯一性
Existence and Uniqueness of Solutions for a Class of Chemically Active Fluid Equations
DOI: 10.12677/aam.2024.134119, PDF,    科研立项经费支持
作者: 王长佳, 苏日娜*：长春理工大学数学与统计学院，吉林 长春
关键词: 非牛顿流；化学活性流体；存在性；唯一性；Non-Newtonian Fluids； Chemically Active Fluid； Existence； Uniqueness
摘要: 本文拟在三维光滑有界区域Ω中，考虑一类稳态非牛顿化学活性流体运动方程组的第一边值问题。在外力项某一范数适当小的条件下，用迭代方法证明了当指数时方程组正则解的存在唯一性。
Abstract: In this paper, we consider the first boundary value problem for a class of steady non-Newtonian chemically active fluid equations in a three-dimensional smooth bounded domain Ω. When exponent , the existence and uniqueness of the regular solutions for the problem was proved by iterative method under the condition that the norm of the external force term is properly small.
文章引用：王长佳, 苏日娜. 一类化学活性流体方程组解的存在唯一性[J]. 应用数学进展, 2024, 13(4): 1292-1307. https://doi.org/10.12677/aam.2024.134119

参考文献

[1] Rojas-Medar, M.A. and Lorca, S.A. (1995) the Equations of a Viscous Incompressible Chemical Active Fluid I: Uniqueness and Existence of the Local Solutions. Revista de Matemáticas Aplicades, 16, 57-80.
[2] Rojas-Medar, M.A. and Lorca, S.A. (1995) The Equations of a Viscous Incompressible Chemical Active Fluid II: Regularity of Solutions. Revista de Matemáticas Aplicades, 16, 81-95.
[3] Lorca, S.A. and Rojas-Medar, M.A. (1996) Weak Solutions for the Viscous Incompressible Chemically Active Fluids. Revista de Matematica e Estatistica, 14, 183-199.
[4] Rojas-Medar, M.A. and Lorca, S.A. (1995) Global Strong Solution of the Equations for the Motion of a Chemical Active Fluid. Sociedade Brasileira de Matemática, Matemática Contemporânea, 8, 319-335. [Google Scholar] [CrossRef] 
[5] Malham, S. and Xin, J.X. (1998) Global Solutions to a Reactive Boussinesq System with Front Data on an Infinite Domain. Communications in Mathematical Physics, 193, 287-316. [Google Scholar] [CrossRef] 
[6] Ko, S. (2022) Existence of Global Weak Solutions for Unsteady Motions of Incompressible Chemically Reacting Generalized Newtonian Fluids. Journal of Mathematical Analysis and Applications, 513, Article No. 126206. [Google Scholar] [CrossRef] 
[7] Boling, G. and Yadong, S. (2002) The Periodic Initial Value Problem and Initial Value Problem for the Modified Boussinesq Approximation. Journal of Partial Differential Equations, 15, 57-71. [Google Scholar] [CrossRef] 
[8] Lin, W., Guo, B.L. and Shang, Y.D. (2003) The Periodic Initial Value Problem and Initial Value Problem for the Non-Newtonian Boussinesq Approximation. Applicable Analysis, 82, 787-808. [Google Scholar] [CrossRef] 
[9] 杨惠, 王长佳. 一类稳态不可压非牛顿Boussinesq方程组解的存在唯一性[J]. 吉林大学学报(理学版), 2019, 57(4): 753-761.
[10] 王爽, 王长佳. 一类各向异性非牛顿Boussinesq方程组弱解的存在性研究[J]. 应用数学进展, 2022, 11(1): 450-461. [Google Scholar] [CrossRef] 
[11] 刘琳, 王长佳. 一类不可压非牛顿Boussinesq方程组正则解的存在性[J]. 应用数学进展, 2023, 12(4): 1855-1865. [Google Scholar] [CrossRef] 
[12] Sohr, H. (2001) The Navier-Stokes Equations: an Elementary Analytic Approach. Birkhäuser, Basel. [Google Scholar] [CrossRef] 
[13] Paré, S.C. (1992) Existence, Uniqueness and Regularity of Solution of the Equations of a Turbulence Model for Incompressible Fluids. Applicable Analysis, 43, 245-296. [Google Scholar] [CrossRef] 
[14] Nečas, J. (1965) Equations aux DeriveesPartielles. Presses de I’Universite de Montreal, Montreal.
[15] Crispo, F. and Grisanti, C.R. (2008) On the Existence, Uniqueness and Regularity for a Class of Shear-Thinning Fluids. Journal of Mathematical Fluid Mechanics, 10, 455-487. [Google Scholar] [CrossRef] 
[16] Ebmeyer, C. (2006) Regularity in Sobolev Spaces of Steady Flows of Fluids with Shear-Dependent Viscosity. Mathematical Methods in the Applied Sciences, 29, 1687-1708. [Google Scholar] [CrossRef] 

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