大尺度湿大气原始方程组对边界参数的连续依赖性

郭连红; 李远飞

doi:10.21656/1000-0887.410028

大尺度湿大气原始方程组对边界参数的连续依赖性

doi: 10.21656/1000-0887.410028

广东财经大学华商学院应用数学系, 广州 511300

基金项目: 广东普通高校重点科研项目(自然科学)(2019KZDXM042)

详细信息

作者简介:
郭连红(1982—),女，副教授,硕士(通讯作者. E-mail: guoat164@163.com);李远飞(1982—),男，特聘教授,博士(E-mail: liqfd@163.com).

中图分类号: O178
计量
- 文章访问数: 2924
- HTML全文浏览量: 240
- PDF下载量: 326
- 被引次数: 0
出版历程
- 收稿日期: 2020-01-13
- 修回日期: 2020-07-10
- 刊出日期: 2020-09-01

Continuous Dependence on Boundary Parameters of the Original Equations for LargeScale Wet Atmosphere

Department of Applied Mathematics, Huashang College, Guangdong University of Finance & Economics, Guangzhou 511300, P.R.China

Funds: The National Natural Science Foundation of China(11371175)

摘要

摘要: 大气的大尺度动力学方程由Navier-Stokes方程导出的原始方程组控制,并与热力学和盐度扩散输运方程耦合.在过去的几十年里,人们从数学的角度对大气、海洋与耦合了大气和海洋的原始方程组进行了广泛的研究.许多学者的研究主要关注原始方程组在数学上的逻辑性，即方程组的适定性.笔者开始注意到研究原始方程组自身稳定性的必要性.因为在模型建立、简化的过程中不可避免地会出现一些误差,这就需要研究方程组中系数的微小变化是否会引起方程组解的巨大变化.该文运用原始方程组解的先验估计,结合能量估计与微分不等式技术,展示了如何控制水汽比,证明了大尺度湿大气原始方程组的解对边界参数的连续依赖性.
- 原始方程组 /
- 先验估计 /
- 连续依赖性
Abstract: Large-scale dynamic equations for atmosphere are controlled by the original equations derived from the Navier-Stokes equations, and coupled with the thermodynamics and salinity diffusion transport equations. In the past few decades, the atmosphere, ocean, and atmosphere-ocean coupling original equations were extensively studied from the perspective of mathematics. The previous literatures mainly focused on the mathematical logic or well-posedness of the original equations. The stability of the original equations was addressed. Given the inevitable errors in the model establishment and simplification, the effects of coefficients’ small changes on solutions’ great changes were studied for the original equations. Prior estimates of the solutions, combined with energy estimation and the differential inequality technique, were used to control steam ratios. The results prove the continuous dependence of the solutions to the large-scale wet atmosphere original equations on boundary parameters.
- original equation /
- prior estimation /
- continuous dependence

HTML全文

参考文献(28)

[1]	BABIN A, MAHALOV A, NICOLAENKO B. Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics[J]. ESAIM Mathematical Modelling and Numerical Analysis,2000,34(2): 201-222.
[2]	EWALDY B D, TEMAM R. Maximum principles for the primitive equations of the atmosphere[J]. Discrete and Continuous Dynamical Systems A,2001,7(2): 343-362.
[3]	GUO B L, HUANG D W. Existence of weak solutions and trajectory attractors for the moist atmospheric equations in geophysics[J]. Journal of Mathematical Physics,2006,47: 1089-7658.
[4]	LIONS J L, TEMAM R, WANG S. On the equations of the large-scale ocean[J]. Nonlinearity,1992,5: 1007-1053.
[5]	LIONS J L, TEMAM R, WANG S. New formulations of the primitive equations of atmosphere and applications[J]. Nonlinearity,1992,5: 237-288.
[6]	CAO C S, LI J K, TITI E S. Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity[J]. Journal of Differential Equations,2014,257(11): 4108-4132.
[7]	CAO C S, LI J K, TITI E S. Local and global well-posedness of strong solutions to the 3D primitive equations with vertical eddy diffusivity[J]. Archive for Rational Mechanics and Analysis,2014,214(1): 35-76.
[8]	ZELATI M C, FREMOND M, TEMAM R, et al. The equations of the atmosphere with humidity and saturation: uniqueness and physical bounds[J]. Physica D: Nonlinear Phenomena,2013,264: 49-65.
[9]	ZELATI M C, HUANG A, KUKAVICA I, et al. The primitive equations of the atmosphere in presence of vapour saturation[J]. Nonlinearity,2015,28(3): 625-668.
[10]	PETCU M, TEMAM R M, ZIANE M. Some mathematical problems in geophysical fluid dynamics[J]. Handbook of Mathematical Fluid Dynamics,2009,14: 577-750.
[11]	CAO C S, TITI E S. Global well-posedness and finite dimensional global attractor for a 3D planetary geostrophic viscous model[J]. Communications on Pure and Applied Mathematics,2003,56(2): 198-233.
[12]	CAO C S, TITI E S, ZIANE M. A “horizontal” hyper-diffusion 3-D thermocline planetary geostrophic model: well-posedness and long-time behavior[J]. Nonlinearity,2004,17: 1749-1776.
[13]	JU N, TEMAM R. Finite dimensions of the global attractor for 3D primitive equations with viscosity[J]. Journal of Nonlinear Science,2015,25(1): 131-155.
[14]	GUILLN-GONZLEZ F, MASMOUDI N, RODRGUEZ-BELLIDO M A. Anisotropic estimates and strong solutions for the primitive equations[J]. Differential and Integral Equations,2001,14: 1381-1408.
[15]	GUO B, HUANG D. Existence of weak solutions and trajectory attractors for the moist atmospheric equations in geophysics[J]. Journal of Mathematical Physics,2006,47(8): 083508.
[16]	YOU B, LI F. Global and exponential attractors of the three dimensional viscous primitive equations of large-scale moist atmosphere[R/OL]. 2016. [2020-07-10]. https://arxiv.org/pdf/1610.07283. pdf.
[17]	GUO B, HUANG D. Existence of the universal attractor for the 3D viscous primitive equations of large-scale moist atmosphere[J]. Journal of Differential Equations,2011,251(3): 457-491.
[18]	KUKAVICA I, ZIANE M. On the regularity of the primitive equations of the ocean[J]. Nonlinearity,2007,20(12): 2739-2753.
[19]	黄代文, 郭柏灵. 关于海洋动力学中二维的大尺度原始方程组[J]. 应用数学和力学, 2007,28(5): 521-531.(HUANG Daiwen, GUO Boling. On the two-dimensional large-scale primitive equations in oceanic dynamics[J]. Applied Mathematics and Mechanics,2007,28(5): 521-531.(in Chinese))
[20]	黄代文, 郭柏灵. 关于海洋动力学中二维的大尺度原始方程组[J]. 应用数学和力学, 2007,28(5): 532-538.(HUANG Daiwen, GUO Boling. On the two-dimensional large-scale primitive equations in oceanic dynamics[J]. Applied Mathematics and Mechanics,2007,28(5): 532-538.(in Chinese))
[21]	李盼晓. 非局部时滞反应扩散方程波前解的指数稳定性[J]. 应用数学和力学, 2018,39(11): 1300-1312.(LI Panxiao. Exponential stability of traveling wavefronts for reaction diffusion equations with delayed nonlocal responses[J]. Applied Mathematics and Mechanics,2018,39(11): 1300-1312.(in Chinese))
[22]	EVANS L C, GASTLER R. Some results for the primitive equations with physical boundary conditions[J]. Zeitschrift für Angewandte Mathematik und Physik,2013,64(6): 1729-1744.
[23]	CICHON M, STRAUGHAN B, YANTIR A. On continuous dependence of solutions of dynamic equations[J]. Applied Mathematics and Computation,2015,252: 473-483.
[24]	李远飞. 原始方程组对粘性系数的连续依赖性[J]. 山东大学学报(理学版), 2019,54(12): 12-23.(LI Yuanfei. Continuous dependence on viscosity coefficient for primitive equations[J]. Journal of Shandong University (Science Edition),2019,54(12): 12-23.(in Chinese))
[25]	李远飞, 郭连红. 具有边界反应Brinkman-Forchheimer型多孔介质的结构稳定性[J]. 高校应用数学学报, 2019,34(3): 315-324.(LI Yuanfei, GUO Lianhong. Structural stability of Brinkman-Forchheimer porous media with boundary reaction[J]. Applied Mathematics: a Journal of Chinese Universities,2019,34(3): 315-324.(in Chinese))
[26]	BABIN A V, VISHIK M I. Attractors of Evolution Equations [M]. Amsterdam: North-Holland, 1992.
[27]	CAO C S, TITI E S. Global well-posedness of the three-dimensional viscous primitive equations of large-scale ocean and atmosphere dynamics[J]. Annals of Mathematics,2007,166: 245-267.
[28]	LIN C H, PAYNE L E. Continuous dependence on the soret coefficient for double diffusive convection in darcy flow[J]. Journal of Mathematical Analysis and Applications,2008,342(1): 311-325.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 2924
HTML全文浏览量: 240
PDF下载量: 326
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

大尺度湿大气原始方程组对边界参数的连续依赖性

doi: 10.21656/1000-0887.410028

作者简介:
郭连红(1982—),女，副教授,硕士(通讯作者. E-mail: guoat164@163.com);李远飞(1982—),男，特聘教授,博士(E-mail: liqfd@163.com).

计量

Continuous Dependence on Boundary Parameters of the Original Equations for LargeScale Wet Atmosphere

计量

目录

留言板

大尺度湿大气原始方程组对边界参数的连续依赖性

doi: 10.21656/1000-0887.410028

作者简介: 郭连红(1982—),女，副教授,硕士(通讯作者. E-mail: guoat164@163.com);李远飞(1982—),男，特聘教授,博士(E-mail: liqfd@163.com).

计量

出版历程

Continuous Dependence on Boundary Parameters of the Original Equations for LargeScale Wet Atmosphere

计量

出版历程

目录

作者简介:
郭连红(1982—),女，副教授,硕士(通讯作者. E-mail: guoat164@163.com);李远飞(1982—),男，特聘教授,博士(E-mail: liqfd@163.com).