Artículo
Stability of fractionally dissipative 2D quasi-geostrophic equation with infinite delay
Autor/es | Liang, Tongtong
Caraballo Garrido, Tomás Wang, Yejuan |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2020-08-18 |
Fecha de depósito | 2022-03-03 |
Publicado en |
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Resumen | In this paper, fractionally dissipative 2D quasi-geostrophic equations with an external force containing infinite delay is considered in the space Hs with s ≥ 2 − 2α and α ∈ ( 1 2 , 1). First, we investigate the existence ... In this paper, fractionally dissipative 2D quasi-geostrophic equations with an external force containing infinite delay is considered in the space Hs with s ≥ 2 − 2α and α ∈ ( 1 2 , 1). First, we investigate the existence and regularity of solutions by Galerkin approximation and the energy method. The continuity of solutions with respect to initial data and the uniqueness of so lutions are also established. Then we prove the existence and uniqueness of a stationary solution by the Lax-Milgram theorem and the Schauder fixed point theorem. Using the classical Lyapunov method, the construction method of Lyapunov functionals and the Razumikhin-Lyapunov technique, we analyze the local stability of stationary solutions. Finally, the polynomial stability of stationary solutions is verified in a particular case of unbounded variable delay. |
Cita | Liang, T., Caraballo Garrido, T. y Wang, Y. (2020). Stability of fractionally dissipative 2D quasi-geostrophic equation with infinite delay. Journal of Dynamics and Differential Equations, 33 (4), 2047-2074. |
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