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        一類微極流體方程組強(qiáng)解的存在唯一性

        2020-03-30 21:56:11史偉偉

        摘 要:在二維或三維光滑有界區(qū)域中,考慮一類微極流體方程組的第一邊值問題,在外力項(xiàng)的某一范數(shù)適當(dāng)小的條件下,用不動(dòng)點(diǎn)定理證明了當(dāng)指數(shù)p>1時(shí)方程組強(qiáng)解的存在唯一性.

        關(guān)鍵詞:微極流體方程;強(qiáng)解;存在唯一性

        中圖分類號:O175.2 文獻(xiàn)標(biāo)識(shí)碼:A 文章編號:

        參考文獻(xiàn)

        [1] Eringen A C. Simple microfluids[J]. International Journal of Engineering Science,1964,2(2):205-217.

        [2] M?alek J,Neˇcas J,Rokyta M,Ru˙ˇziˇcka M. Weak and measure-valued solutions to evolutionary partial differential equations[M]. Applied Mathematics and Mathematical Computation,1996.

        [3] Bellout H, Bloom F, Neˇcas J. Young measure-valued solutions for non-newtonian incompressible fluids[J]. Communications in Partial Differential Equations,1994,19(11-12):1763-1803.

        [4] Diening L,Ru˙ˇziˇcka M. Strong solutions for generalized Newtonian fluids[J]. Journal of Mathematical Fluid Mechanics,2005,7(3):413-450.

        [5] Berselli L C,Diening L,Ru˙ˇziˇcka M. Existence of strong solutions for incompressible fluids with shear dependent viscosities[J]. Journal of Mathematical Fluid Mechanics,2010,12(1):101-132.

        [6] M?alek J,Neˇcas J,Ru˙ˇziˇcka M. On weak solutions to a class of non-Newtonian incompressible fluids in bounded three-dimensional domains:the casa p 2[J]. Advances in Difference Equations,2001,6(3):257-302.

        [7] Amman H. Stability of the rest state of viscous incompressible fluid[J]. Archive for Rational Me- chanics and Analysis,1994,126(3):231-242.

        [8] Bothe D,Pruss J. Lp-theory for a class of non-Newtonian fluids[J]. SIAM Journal on Mathematical Analysis,2007,39(2):379-421.

        [9] Galdi G P. An introduction to the mathematical theory of the Navier-Stokes Equations[M]. New York:Springer,1994.

        [10] Arada N. A note on the regularity of flows with shear-dependent viscosity[J]. Nonlinear Analysis:Theory,Methods & Applications,2012,75(14):5401-5415.

        [11] Kreml O, Pokorny? M. On the local strong solutions for the FENE dumbbell model[J]. Discrete Contin. Dyn. Syst. Ser. S,2010,3(2):311-324.

        [12] SUN Yongzhong,WANG Chao,ZHANG Zhifei. A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations[J]. Journal de Math?ematiques Pures et Appliqu?ees,2011,95(1):36-47.

        作者簡介;史偉偉(1994~),女,漢族:碩士研究生,從事偏微分方程的研究。

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