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带有Power-Law型粘性项的可压缩非牛顿流的光滑解
Classical Solutions to the Compressible Non-Newtonian Fluids with Power-Law Viscous

DOI: 10.12677/PM.2019.93031, PP. 243-253

Keywords: 可压缩非牛顿流,Power-Law 型粘性项,光滑解
Compressible Non-Newtonian Fluids
, Power-Law Viscous, Classical Solution

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Abstract:

本文研究一维有界区间上的可压非牛顿流体模型。在初始密度有正下界的情况下,通过构造逼近解,应用能量估计,得到了带有Power-Law结构粘性项的非牛顿流模型初边值问题光滑解的局部存在性。
In this paper, a one-dimensional compressible non-Newtonian fluid model on a bounded interval is studied. If the initial density has a positive lower bound, the local existence of the classical solutions for the initial boundary value problem of a non-Newtonian fluid model with Power-Law viscous is proved by constructing approximate solutions and applying energy estimation.

References

[1]  Ladyzhenskaya, O.A. (1970) New Equations for the Description of the Motions of Viscous Incompressible Fluids and Global Solva-bility for Their Boundary Value Problems. Trudy Matematicheskogo Instituta imeni V. A. Steklova, 102, 85-104.
[2]  Lions, P.L. (1998) Mathematical Topics in Fluid Mechanics: Compressible Models. Clarendon Press, Oxford.
[3]  Necas, J. (1990) Theory of Multipolar Viscous Fluids. The Mathematics of Finite Elements and Applications, 7, 233-244.
[4]  Necas, J. and Novotny, A. (1994) Measure-Valued Solution for Non-Newtonian Compressible Isothermal Monopolar Fluid. Acta Applicandae Mathematica, 37, 109-128.
https://doi.org/10.1007/BF00995134
[5]  Neckcasova, S. and Lukacova, M. (1994) Bipolar Barotropic Non-Newtonian Fluid. Commentationes Mathematicae Universitatis Carolinae, 35, 467-483.
[6]  Feireisl, E., Liao, X. and Malek, J. (2015) Global Weak Solutions to a Class of Non-Newtonian Compressible Fluids. Mathematical Methods in the Applied Sciences, 38, 3482-3494.
https://doi.org/10.1002/mma.3432
[7]  Mamontov, A.E. (1999) Global Solvability of Multidimensional Navier-Stokes Equations of Compressible Nonlinearly Viscous Fluid. I. Siberian Mathematical Journal, 40, 351-362.
https://doi.org/10.1007/BF02679762 http://apps.webofknowledge.com/full_record.do?product=UA&search_mode=GeneralSearch&qid=4&SID=6Cb5e1i8fXVsPmEc3eL&page=1&doc=1
[8]  Yuan, H.J. and Xu, X.J. (2008) Existence and Uniqueness of Solutions for a Class of Non-Newtonian Fluids with Singularity and Vacuum. Journal of Differential Equations, 245, 2871-2916. http://www.elsevier.com/locate/jde
https://doi.org/10.1016/j.jde.2008.04.013
[9]  Yuan, H.J. and Li, H.P. (2012) Existence and Uniqueness of Solution for a Class of Non-Newtonian Fluids with Vacuum and Damping. Journal of Mathematical Analysis and Applications, 391, 223-239.
https://www.sciencedirect.com/science/article/pii/S0022247X12001084?via%3Dihub
https://doi.org/10.1016/j.jmaa.2012.02.015
[10]  Fang, L. and Li, Z.L. (2015) On the Existence of Local Classical Solution for a Class of One-Dimensional Compressible Non-Newtonian Fluids. Acta Mathematica Scientia (English Series), 35, 157-181.
https://doi.org/10.1016/S0252-9602(14)60148-X
[11]  Fang, L., Guo, Z.H. and Wang, Y.X. (2016) Local Strong Solutions to a Compressible Non-Newtonian Fluid with Density-Dependent Viscosity. Mathematical Methods in the Applied Sciences, 39, 2583-2601.
https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.3714
https://doi.org/10.1002/mma.3714
[12]  杨迪, 佟丽宁. 真空下一维可压的非牛顿Ellis模型解的存在唯一性[J]. 应用数学与计算数学学报, 2017, 31(1): 128-142. http://qikan.cqvip.com/article/detail.aspx?id=671559827
[13]  Yin, L., Xu, X.J. and Yuan, H.J. (2008) Global Existence and Uniqueness of Solution of the Initial Boundary Value Problem for a Class of Non-Newtianian Fluids with Vacuum. Zeitschrift fur Angewandte Mathematik und Physik, 59, 457-474.
https://doi.org/10.1007/s00033-006-5078-7

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