Liouville-Type Theorems for 3D Stationary Tropical Climate Model in Mixed Local Morrey Spaces
Tóm tắt
This paper studies the Liouville-type theorems for stationary tropical climate model on the whole space
$${\mathbb {R}}^3$$
. We introduce the mixed local Morrey space adapted to tropical climate model and then establish Liouville-type conditions in these spaces, which improve previous ones.
Tài liệu tham khảo
Chae, D.: Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations. Commun. Math. Phys. 326, 37–48 (2014)
Chae, D., Wolf, J.: On Liouville type theorems for the steady Navier-S-tokes equations in \({\mathbb{R} }^3\). J. Differ. Equ. 261, 5541–5560 (2016)
Chae, D., Yoneda, T.: On the Liouville theorem for the stationary Navier–Stokes equations in a critical space. J. Math. Anal. Appl. 405, 706–710 (2013)
Chae, D., Wolf, J.: On the Liouville type theorems for self-similar solutions to the Navier–Stokes equations. Arch. Ration. Mech. Anal. 225(1), 549–572 (2017)
Chae, D., Weng, S.: Liouville type theorems for the steady axially symmetric Navier-Stokes and magnetohydrodynamic equations. Discret. Contin. Dynam. Syst. 36(10), 5267–5285 (2016)
Chamorro, D., Jarrín, O., Lemarié-Rieusset, P.G.: Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 38(3), 689–710 (2021)
Ding, H., Wu, F.: The Liouville theorems for 3D stationary tropical climate model. Math. Methods Appl. Sci. 44(18), 14437–14450 (2021)
Galdi, G.P.: An Introduction to the Mathematical Theory of the Navier–Stokes Equations Steady-state problems. Second edition Monographs in Mathematics. Springer, New York (2011)
Jarrín O. Descriptions déterministes de la turbulence dans les équations de Navier-Stokes. Ph.D. thesis, Paris-Saclay University, Paris, France, 2018
Jarrín, O.: Liouville theorems for a stationary and non-stationary coupled system of liquid crystal flows in local Morrey spaces. J. Math. Fluid Mech. 24(2), 1–29 (2022)
Jarrín, O.: A remark on the Liouville problem for stationary Navier–Stokes equations in Lorentz and Morrey spaces. J. Math. Anal. Appl. 486(1), 123871 (2020)
Jleli, M., Ragusa, M.A., Samet, B.: Nonlinear Liouville-type theorems for generalized Baouendi-Grushin operator on Riemaniann manifolds. Adv. Differ. Equ. 28(1–2), 143–168 (2023)
Koch, G., Nadirashvili, N., Seregin, G., et al.: Liouville theorems for the Navier-Stokes equations and applications. Acta Math. 203(1), 83–105 (2009)
Kozono, H., Terasawab, Y., Wakasugib, Y.: A remark on Liouville-type theorems for the stationary Navier–Stokes equations in three space dimensions. J. Funct. Anal. 272, 804–818 (2017)
Leray J. Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l’hydrodynamique, 1933
Li, J., Zhai, X., Yin, Z.: On the global well-posedness of the tropical climate model. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 99(6), e201700306 (2019)
Li, J., Titi, E.S.: Global well-posedness of strong solutions to a tropical climate model. Discret. Contin. Dynam. Syst. 36(8), 4495–4516 (2016)
Li, Z.X., Deng, L.H., Shang, H.F.: Global well-posedness and large time decay for the d-dimensional tropical climate model. AIMS Math. 6(6), 5581–5595 (2021)
Fernández-Dalgo, P.G., Jarrin, O.: Weak-strong uniqueness in weighted \(L^2\) spaces and weak suitable solutions in local Morrey spaces for the MHD equations. J. Differ. Equs. 271, 864–915 (2021)
Fernández-Dalgo, P.G., Jarrin, O.: Discretely self-similar for 3D MHD equations and global weak solutions in the weighted \(L^2\) space. J. Math. Fluid Mech. 23(1), 1–30 (2021)
Li, Z., Su, Y.: Liouville type theorems for the stationary Hall-magnetohydrodynamic equations in local Morrey spaces. Math. Meth Appl. Sci. 45(17), 10891–10903 (2022)
Seregin, G.: Liouville type theorem for stationary Navier–Stokes equations. Nonlinearity 29, 2191–2195 (2016)
Seregin G.A.: Liouville type theorem for steady-state Navier-Stokes equations. Journées équations aux dérivées partielles, 2016: 1-5
Seregin, G., Wang, W.: Sufficient conditions on Liouville type theorems for the 3D steady Navier–Stokes equations. St. Petersburg Math. J. 31(2), 387–393 (2020)
Scapellato A.: On some qualitative results for the solution to a Dirichlet problem in local generalized Morrey spaces, Book Series AIP Conf. Proc., art.n. 020138, vol. 1798, https://doi.org/10.1063/1.4972730,2017
Wu, F.: Regularity criteria for the 3D tropical climate model in Morrey–Campanato space. Electron. J. Qual. Theory Differ. Equ. 2019(48), 1–11 (2019)
Ye, Z.: Global regularity for a class of 2D tropical climate model. J. Math. Anal. Appl. 446(1), 307–321 (2017)
Yuan, B., Wang, F.: The Liouville theorems for 3D stationary tropical climate model in local Morrey spaces. Appl. Math. Lett. 2022, 108533