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一类不可压非牛顿Boussinesq方程组正则解的存在性
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Abstract:
在三维光滑有界区域中研究了奇异情况下的非牛顿Boussinesq方程组的周期初边值问题。应用Galerkin方法、Gronwall不等式、Aubin-Lions引理，并结合能量估计、紧性方法证明了外力项适当小的情况下，该方程组正则解的存在性。
The periodic initial boundary value problem of non-Newtonian Boussinesq equations in singular case is studied in three-dimensional smooth bounded domain. By using Galerkin method, Gronwall inequality, Aubin-Lions lemma, energy estimation and compactness method, the existence of regu-lar solutions for the system is proved when the external force term is appropriately small.
| [1] | 张能球. 几类流体力学方程组的解的适定性[D]: [博士学位论文]. 上海: 华东理工大学, 2021. |
| [2] | Majda, A.J., Bertozzi, A.L. and Ogawa, A. (2002) Vorticity and Incompressible Flow. Cambridge Texts in Applied Mathematics. Ap-plied Mechanics Reviews, 55, B77-B78. https://doi.org/10.1115/1.1483363 |
| [3] | Pedlosky, J. (1897) Geophysical Fluid Dynamics. Springer, New York. |
| [4] | Ladyzhenskaya, O.A. (1969) The Mathematical Theory of Viscous Incom-pressible Flow. Gordon and Breach, New York. |
| [5] | Lions, J.L. (1969) Quelquesméthodes de résolution des probémes aux limites non lineáires. Dunod, Paris. |
| [6] | Bellout, H., Bloom, F. and Ne？as, J. (1994) Young Measure-Valued Solu-tions for Non-Newtonian Incompressible Fluids. Communications in Partial Differential Equations, 19, 1763-1803.
https://doi.org/10.1080/03605309408821073 |
| [7] | Málek, J., Ne？as, J. and R？？i？ka, M. (1993) On the Non-Newtonian Incompressible Fluids. Mathematical Models and Methods in Applied Sciences, 3, 35-63. https://doi.org/10.1142/S0218202593000047 |
| [8] | Frehse, J., Málek, J. and Steinhauer, M. (2000) On Existence Results for Fluids with Shear Dependent Viscosity-Unsteady Flows. Partial Differential Equations, Routledge, Oxford-shire, 121-129.
https://doi.org/10.1201/9780203744376-12 |
| [9] | Málek, J., Ne？as, J. and R？？i？ka, M. (2001) On Weak Solutions to a Class of Non-Newtonian Incomepressible Fluids in Bounded Three-Dimensional Domains: The Case p≥2. Advances in Differential Equations, 6, 257-302.
https://doi.org/10.57262/ade/1357141212 |
| [10] | Boling, G. and Yadong, S. (2002) The Periodic Initial Value Prob-lem and Initial Value Problem for the Modified Boussinesq Approximation. Journal of Partial Differential Equations, 15, 57-71. |
| [11] | 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. |
| [12] | Necas, J., Málek, J., Rokyta, M., et al. (2019) Weak and Measure-Valued Solutions to Evolutionary PDEs. Chapman and Hall, London. https://doi.org/10.1201/9780367810771 |
