EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 26 (2022) ESAIM: PS, 26 (2022) 243-264 References
Open Access
Issue
ESAIM: PS
Volume 26, 2022
Page(s) 243 - 264
DOI https://doi.org/10.1051/ps/2022006
Published online 20 May 2022
  1. H. Bessaih and A. Millet, On stochastic modified 3D Navier-Stokes equations with anisotropic viscosity. J. Math. Anal. Appl. 462 (2018) 915–956. [CrossRef] [MathSciNet] [Google Scholar]
  2. D. Bresch, F. Guillén-González, N. Masmoudi and M.A. Rodríguez-Bellido, On the uniqueness of weak solutions of the twodimensional primitive equations. Differ. Integr. Equ. 162 (2003) 77–94. [Google Scholar]
  3. Z. Brzeéniak and E. Motyl, Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D domains. J. Differ. Equ. 254 (2013) 1627–1685. [CrossRef] [Google Scholar]
  4. Z. Brzeéniak and M. Ondrejat, Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces. Ann. Probab. 41 (2013) 1938–1977. [MathSciNet] [Google Scholar]
  5. C. Cao, S. Ibrahim, K. Nakanishi and E.S. Titi, Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics. Comm. Math. Phys. 337 (2015) 473–482. [CrossRef] [MathSciNet] [Google Scholar]
  6. C. Cao, J. Li and E.S. Titi, Global well-posedness of the 3D primitive equations with only horizontal viscosity and diffusivity. Commun. Pure Appl. Math. 69 (2016) 1492–1531. [CrossRef] [Google Scholar]
  7. C. Cao, J. Li and E.S. Titi, Strong solutions to the 3D primitive equations with only horizontal dissipation: near H1 initial data. J. Funct. Anal. 272 (2017) 4606–4641. [CrossRef] [MathSciNet] [Google Scholar]
  8. C. Cao and E. Titi, Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Ann. Math. 166 (2007) 245–267. [CrossRef] [MathSciNet] [Google Scholar]
  9. B. Cushman-Roisin and J.M. Beckers, Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects. Academic Press (2007). [Google Scholar]
  10. A. Debussche, N. Glatt-Holtz and R. Temam, Local martingale and pathwise solutions for an abstract fluids model. Physica D 240 (2011) 1123–1144. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Debussche, N. Glatt-Holtz, R. Temam and M. Ziane, Glabal existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplitive white noise. Nonlinearity 316 (2012) 723–776. [Google Scholar]
  12. Z. Dong, J. Zhai and R. Zhang, Large deviation principles for 3D stochastic primitive equations. J. Differ. Equ. 263 (2017) 3110–3146. [CrossRef] [Google Scholar]
  13. Z. Dong and R. Zhang, On the small time asymptotics of 3D stochastic primitive equations. Math Meth Appl Sci. (2018) 1–1. [Google Scholar]
  14. B. Ewald, M. Petcu and R. Temam, Stochastic solutions of the two-dimensional primitive equations of the ocean and atmospherewith an additive noise. Anal. Appl. 5 (2007) 183–198. [CrossRef] [Google Scholar]
  15. H. Gao and C. Sun, Random attractor for the 3d viscous stochastic primitive equations with additive noise. Stoch. Dyn. 9 (2009) 293–313. [CrossRef] [Google Scholar]
  16. H. Gao and C. Sun, Well-posedness and large deviations for the stochastic primitive equations in two space dimensions. Commu. Math. Sci. 10 (2012) 233–273. [Google Scholar]
  17. N. Glatt-Holtz, I. Kukavica, V. Vicol and M. Ziane, Existence and regularity of invariant measures for the three dimensinonal stochastic primitive equations. J. Math. Phys. 55 (2014) 051504. [CrossRef] [MathSciNet] [Google Scholar]
  18. N. Glatt-Holtz and R. Temam, Pathwise solutions of the 2-d stochastic primitive equations. Appl. Math. Optim. 63 (2011) 401–433. [CrossRef] [MathSciNet] [Google Scholar]
  19. N. Glatt-Holtz and M. Ziane, The stochastic primitive equations in two space dimensions with multiplicative noise. DCDS- Series B 10 (2008) 801–822. [CrossRef] [Google Scholar]
  20. B. Goldys, M. Röckner and X. Zhang, Martingale solutions and Markov selections for stochastic partial differential equations. Stoch. Process. Appl. 119 (2009) 1725–1764. [CrossRef] [Google Scholar]
  21. F. Guillen-Gonzalez, N. Masmoudi and M.A. Rodriguez-Bellido, Anisotropic estimates and strong solutions of the primitive equations. Differ. Integral Eqns. 14 (2001) 1381–1408. [Google Scholar]
  22. B. Guo and D. Huang, 3d stochastic primitive equations of the large-scale oceans: global well-posedness and attractors. Comm. Math. Phys. 286 (2009) 697–723. [CrossRef] [MathSciNet] [Google Scholar]
  23. I. Gyöngy and N. Krylov, Existence of strong solutions for Ito’s stochastic equations via approximations. Probab. Theory Related Fields 105 (1996) 143–158. [CrossRef] [MathSciNet] [Google Scholar]
  24. D. Han-Kwan and T.T. Nguyen, Ill-posedness of the hydrostatic euler and singular Vlasov equations. Arch. Ratl. Mech. Anal. 221 (2016) 1317–1344. [CrossRef] [Google Scholar]
  25. M. Hieber and A. Hussein, An approach to the primitive equations for oceanic and atmospheric dynamics by evolution equations, Fluids under pressure. Adv. Math. Fluid Mech., Birkhöuser/Springer, Cham (2020) 1–1. [Google Scholar]
  26. C. Hu, R. Temam and M. Ziane, Regularity results for linear elliptic problems related to the primitive equations. Chin. Ann. Math. Ser. B 23 (2002) 277–292. [CrossRef] [Google Scholar]
  27. A. Hussein, Partial and full hyper-viscosity for Navier-Stokes and primitive equations. J. Differ. Equ. 269 (2020) 3003–3030. [CrossRef] [Google Scholar]
  28. A. Hussein, M. Saal and M. Wrona, Primitive equations with horizontal viscosity: the initial value and the time-periodic problem for physical bound conditions. Discr. Continu. Dyn. Syst. A 41 (2021) 3063–3092. [CrossRef] [Google Scholar]
  29. A. Jakubowski. Short Communication: The almost sure skorokhod representation for subsequences in Nonmetric spaces. Theory Probab. Appl. 42 (1998) 167–175. [CrossRef] [Google Scholar]
  30. N. Ju, On H2 solutions and z-weak solutions of the 3D primitive equations. Mathematics 66 (2015) 973–996. [Google Scholar]
  31. N. Ju, Uniqueness of some weak solutions for 2D viscous primitive equations. J. Math. Fluid Mech. 23 (2021) 1–29. [CrossRef] [Google Scholar]
  32. G.M. Kobelkov, Existence of a solution 'in the large’ for ocean dynamics equations. J. Math. Fluid Mech. 9 (2007) 588–610. [CrossRef] [MathSciNet] [Google Scholar]
  33. G.M. Kobelkov, Existence of a solution in the large for the 3D large-scale ocean dynamics equations. C.R. Math. Acad. Sci. Paris 343 (2006) 283–286. [CrossRef] [MathSciNet] [Google Scholar]
  34. I. Kukavica, Y. Pei, W. Rusin and M. Ziane, Primitive equations with continuous initial data. Nonlinearity 27 (2014) 1135–1155. [CrossRef] [MathSciNet] [Google Scholar]
  35. I. Kukavica, R. Temam, V. Vicol and M. Ziane, Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. J. Differ. Equ. 250 (2011) 1719–1746. [CrossRef] [Google Scholar]
  36. I. Kukavica and M. Ziane, On the regularity of the primitive equations of the ocean. Nonlinearity 20 (2007) 2739–2753. [CrossRef] [MathSciNet] [Google Scholar]
  37. J. Li and E. Titi, Existence and uniqueness of weak solutions to viscous primitive equations for a certain class of discontinuous initial data. SIAM J. Math. Anal. 49 (2017) 1–28. [CrossRef] [MathSciNet] [Google Scholar]
  38. J. Li, E. Titi and G. Yuan, The primitive equations approximation of the anisotropic horizontally viscous 3D Navier-Stokes equations. J. Differ. Equ. 306 (2022) 492–524. [CrossRef] [Google Scholar]
  39. S. Liang, P. Zhang and R. Zhu. Determinstic and stochastic 2d Navier-Stokes equations with anisotropic viscosity. J. Differ. Equ. 275 (2021) 473–508. [CrossRef] [Google Scholar]
  40. J.L. Lions, R. Temam and S. Wang, Models for the coupled atmosphere and ocean. Elsevier Science Publishers B.V. 1 (1993) 3–3. [Google Scholar]
  41. J.L. Lions, R. Temam and S. Wang. New formulations of the primitive equations of atmosphere and applications. Nonlinearity 5 (1992) 237–288. [CrossRef] [MathSciNet] [Google Scholar]
  42. J.L. Lions, R. Temam and S. Wang. On the equations of the large-scale ocean. Nonlinearity 5 (1992) 1007–1053. [CrossRef] [MathSciNet] [Google Scholar]
  43. W. Liu and M. Röckner, Stochastic Partial Differential Equations: An Introduction[M]. Springer International Publishing (2015). [Google Scholar]
  44. T.T. Medjo, On the uniqueness of z-weak solutions of the three dimensional primitive equations of the ocean. Nonlinear Anal. Real World Appl. 11 (2010) 1413–1421. [CrossRef] [MathSciNet] [Google Scholar]
  45. R. Mikulevicius and B. Rozovskii, On Equations of Stochastic Fluid Mechanics. Birkhauser Boston (2001). [Google Scholar]
  46. J. Pedlosky, Geophysical Fluid Dynamics. Springer-Verlag, New York (1987). [Google Scholar]
  47. M. Petcu, On the backward uniqueness of the primitive equations. J. Math. Pures Appl. 87 (2007) 275–289. [CrossRef] [MathSciNet] [Google Scholar]
  48. M. Petcu, R. Temam and D. Wirosoetisno, Existence and regularity results for the primitive equations in two space dimensions. Comm. Pure Appl. Anal. 3 (2004) 115–131. [CrossRef] [Google Scholar]
  49. M. Petcu, R. Temam and M. Ziane, Some mathematical problems in geophysical fluid dynamics. Handbook of Numerical Analysis 14 (2009) 577–750. [CrossRef] [Google Scholar]
  50. M. Saal and J. Slavk, Stochastic primitive equations with horizontal viscosity and diffusivity. Preprint arXiv:2109.14568 (2021). [Google Scholar]
  51. C. Sun and H. Gao, Well-posedness for the stochastic 2D primitive equations with Lévy noise. Science China Math. 56 (2013) 1629–1645. [CrossRef] [MathSciNet] [Google Scholar]
  52. T.K. Wong. Blowup of solutions of the hydrostatic Euler equations. Proc. Amer. Math. Soc. 143 (2015) 1119–1125. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.