Article
Trajectory statistical solutions and Liouville type equations for evolution equations: abstract results and applications
Author/s | Zhao, Caidi
Li, Yanjiao Caraballo Garrido, Tomás ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2020-06 |
Deposit Date | 2020-09-08 |
Published in |
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Abstract | In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the existence of trajectory statistical solutions for autonomous evolution equations. Then we establish that ... In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the existence of trajectory statistical solutions for autonomous evolution equations. Then we establish that the constructed trajectory statistical solutions possess invariant property and satisfy a Liouville type equation. Moreover, we reveal that the equation describing the invariant property of the trajectory statistical solutions is a particular situation of the Liouville type equation. Finally, we study the equations of three-dimensional incompressible magneto-micropolar fluids in detail and illustrate how to apply our abstract results to some concrete autonomous evolution equations. |
Funding agencies | National Natural Science Foundation of China European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Ministerio de Ciencia, Innovación y Universidades (MICINN). España |
Project ID. | 11971356
![]() 11271290 ![]() LY17A010011 ![]() PGC2018-096540-B-I00 ![]() |
Citation | Zhao, C., Li, Y. y Caraballo Garrido, T. (2020). Trajectory statistical solutions and Liouville type equations for evolution equations: abstract results and applications. Journal of Differential Equations, 269 (1), 467-494. |
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