Mathematics

Continuous dependence of primitive equations of the atmosphere with vapor saturation

  • Yuanfei LI ,
  • Shengzhong XIAO ,
  • Peng ZENG
Expand
  • 1. School of Data Science, Guangzhou Huashang College, Guangzhou 511300, China
    2. Guangdong AIB Polytechnic, Guangzhou 510507, China

Received date: 2020-03-12

  Online published: 2021-05-26

Abstract

In this paper, we study the primitive equations of the atmosphere in the presence of vapor saturation; these equations are often used in forecasting weather in a cylindrical region. By using the technique of differential inequality and the method of energy estimation, we obtain the prior bounds of the solutions for the equations, and we prove the continuous dependence of the equations on the boundary parameters.

Cite this article

Yuanfei LI , Shengzhong XIAO , Peng ZENG . Continuous dependence of primitive equations of the atmosphere with vapor saturation[J]. Journal of East China Normal University(Natural Science), 2021 , 2021(3) : 34 -46 . DOI: 10.3969/j.issn.1000-5641.2021.03.005

References

1 GILL A E. Atmosphere-Ocean Dynamics [M]. San Diego, CA: Academic Press, 1982.
2 HALTINER G J. Numerical Weather Prediction [M]. New York: Wiley, 1971.
3 HALTINER G J, WILLIAMS R T. Numerical Prediction and Dynamic Meteorology [M]. New York: Wiley, 1980.
4 RICHARDSON L F. Weather Prediction by Numerical Process [M]. Cambridge: Cambridge University Press, 2007.
5 LIONS J L, TEMAM R, WANG S. New formulations of the primitive equations of atmosphere and applications. Nonlinearity, 1992, 5, 237- 288.
6 LIONS J L, TEMAM R, WANG S. On the equations of the large-scale ocean. Nonlinearity, 1992, 5, 1007- 1053.
7 LIONS J L, TEMAM R, WANG S. Mathematical theory for the coupled atmosphere-ocean models (CAO III). J Math Pures Appl, 1995, 74, 105- 163.
8 LIONS J L, TEMAM R, WANG S. Models of the coupled atmosphere and ocean(CAO I). Comput Mech Adv, 1993, (1): 1- 54.
9 郭柏灵, 黄代文, 黄春研. 大气、海洋动力学中一些非线性偏微分方程的研究. 中国科学, 2014, 44 (12): 1275- 1285.
10 ZELATI M C, HUANG A, KUKAVICA, et al. The primitive equations of the atmosphere in presence of vapour saturation. Nonlinearity, 2015, 28 (3): 625- 668.
11 GUO B L, HUANG D W. On the 3D viscous primitive equations of the large-scale atmosphere. Acta Math Sci, 2009, 29 (4): 846- 866.
12 GUO B L, HUANG D W. Existence of the universal attractor for the 3-D viscous primitive equations of large-scale moist atmosphere. Journal of Differential Equations, 2011, 251 (3): 457- 491.
13 SUN J Y, CUI S B. Sharp well-posedness and ill-posedness of the three-dimensional primitive equations of geophysics in Fourier-Besov spaces. Nonlinear Analysis: Real World Applications, 2019, (4): 445- 465.
14 HIEBER M, HUSSEIN A, KASHIWABARA T. Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion . Journal of Differential Equations, 2016, 261 (12): 6950- 6981.
15 YOU B, LI F. Global attractor of the three-dimensional primitive equations of large-scale ocean and atmosphere dynamics. Z Angew Math Phys, 2018, 69, 114.
16 CHIODAROLI E, MICHALEK M. Existence and non-uniqueness of global weak solutions to inviscid primitive and Boussinesq equations. Commun Math Phys, 2017, 353, 1201- 1216.
17 SUN J Y, YANG M. Global well-posedness for the viscous primitive equations of geophysics. Boundary Value Problems, 2016, 2016, 21.
18 GUO B L, HUANG D W, WANG W. Diffusion limit of 3D primitive equations of the large-scale ocean under fast oscillating random force. Journal of Differential Equations, 2015, 259 (6): 2388- 2407.
19 YOU B. Pullback attractor for the three dimensional nonautonomous primitive equations of large-scale ocean and atmosphere dynamics [J]. Comp and Math Methods, 2020, 2(2). DOI: 10.1002/cmm4.1066.
20 李远飞. 原始方程组对粘性系数的连续依赖性. 山东大学学报(理学版), 2019, 54 (12): 12- 23.
21 李远飞. 大尺度海洋大气动力学三维黏性原始方程对边界参数的连续依赖性. 吉林大学学报(理学版), 2019, 57 (5): 1053- 1059.
22 HARDY C H, LITTLEWOOD J E, POLYA G. Inequalities [M]. London: Cambridge University Press, 1953.
23 LIN C, PAYNE L E. Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow. J Math Anal Appl, 2008, 342, 311- 325.
Outlines

/