EXISTENCE AND UNIQUENESS OF LERAY-HOPF SOLUTIONS AND NON-NEGATIVE LERAY-HOPF SOLUTIONS OF DYADIC MODELS FOR THE GENERALIZED NAVIER-STOKES EQUATIONS
Main Article Content
Abstract
In this article, we study the existence and uniqueness of Leray-Hopf solutions and non-negative Leray-Hopf solutions of dyadic models for the 3D generalized Navier-Stokes equations. Our results extend and improve some previous results.
Keywords
Generalized Navier-Stokes equations, Leray-Hopf solutions, non-negative Leray-Hopf solutions.
Article Details
References
[1] A. Cheskidov (2008), Blow-up in finite time for the dyadic model of the Navier-Stokes equations, Trans. Amer. Math. Soc. 360, no. 10, 5101-5120.
[2] Y.Dai,W.Hu, J.Wu and B,Xiao (2020), The Littlewood - Paley decomposition for periodic functions and applications to the Boussinesq equations, Anal. Appl. Singap. 18, no. 4. 639 - 682.
[3] M. Dai (2020), Dyadic models with intermittency dependence for the Hall MHD, arXiv: 2006.15094.
[4] Loukas Grafakos (2008), Classical Fourier analysis, Second edition. Vol. 249. Graduate Texts in Mathematics. New York: Springer.
[5] F.Weisz (2012), Summability of Multi-Dimentional Trigonometric Fourier Series, Surveys in Approximation Theory 17, 1-179.
[6] J.L. Lions (1969), Quelques Méthodes de Resolution des Problèmes aux Limites Non Linéaires, Vol 1. Dunod, Paris.
[7] T. Luo and E. S. Titi (2020), Non-uniqueness of weak solutions to hyperviscous Navier-Stokes equations: on sharpness of J.-L. Lions exponent, Calc. Var. Partial Differential Equations 59, no. 3, Paper No. 92, 15 pp.
[8] N. Katz and N. Pavlović (2005), Finite time blow-up for a dyadic model of the Euler equations, Trans. Amer. Math. Soc., 357 (2): 695-708.
[9] A. M. Obukhov (1971), Some general properties of equations describing the dynamics of the atmosphere, Izv. Akad. Nauk SSSR Ser. Fiz. Atmosfer. i Okeana, 7:695-704.
[10] N. T. Le, L. T. Tinh (2025), On the three dimensional generalized Navier-Stokes equations with damping, Fract. Calc. Appl. Anal.
[11] Phạm Thị Vân, Lê Trần Tình, Lê Thị Mai, Mô hình bài toán rời rạc xấp xỉ phương trình Navier-Stokes bậc phân, Tạp chí Khoa học Trường Đại học Hồng Đức, Số 02, 2024
[12] J. Wu (2003), Generalized MHD equations, Journal of Differential Equations, 195(2), 284-
312.
[2] Y.Dai,W.Hu, J.Wu and B,Xiao (2020), The Littlewood - Paley decomposition for periodic functions and applications to the Boussinesq equations, Anal. Appl. Singap. 18, no. 4. 639 - 682.
[3] M. Dai (2020), Dyadic models with intermittency dependence for the Hall MHD, arXiv: 2006.15094.
[4] Loukas Grafakos (2008), Classical Fourier analysis, Second edition. Vol. 249. Graduate Texts in Mathematics. New York: Springer.
[5] F.Weisz (2012), Summability of Multi-Dimentional Trigonometric Fourier Series, Surveys in Approximation Theory 17, 1-179.
[6] J.L. Lions (1969), Quelques Méthodes de Resolution des Problèmes aux Limites Non Linéaires, Vol 1. Dunod, Paris.
[7] T. Luo and E. S. Titi (2020), Non-uniqueness of weak solutions to hyperviscous Navier-Stokes equations: on sharpness of J.-L. Lions exponent, Calc. Var. Partial Differential Equations 59, no. 3, Paper No. 92, 15 pp.
[8] N. Katz and N. Pavlović (2005), Finite time blow-up for a dyadic model of the Euler equations, Trans. Amer. Math. Soc., 357 (2): 695-708.
[9] A. M. Obukhov (1971), Some general properties of equations describing the dynamics of the atmosphere, Izv. Akad. Nauk SSSR Ser. Fiz. Atmosfer. i Okeana, 7:695-704.
[10] N. T. Le, L. T. Tinh (2025), On the three dimensional generalized Navier-Stokes equations with damping, Fract. Calc. Appl. Anal.
[11] Phạm Thị Vân, Lê Trần Tình, Lê Thị Mai, Mô hình bài toán rời rạc xấp xỉ phương trình Navier-Stokes bậc phân, Tạp chí Khoa học Trường Đại học Hồng Đức, Số 02, 2024
[12] J. Wu (2003), Generalized MHD equations, Journal of Differential Equations, 195(2), 284-
312.