Artículo
Trajectory statistical solutions and Liouville type equations for evolution equations: abstract results and applications
Autor/es | Zhao, Caidi
Li, Yanjiao Caraballo Garrido, Tomás |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2020-06 |
Fecha de depósito | 2020-09-08 |
Publicado en |
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Resumen | 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. |
Agencias financiadoras | National Natural Science Foundation of China European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Ministerio de Ciencia, Innovación y Universidades (MICINN). España |
Identificador del proyecto | 11971356
11271290 LY17A010011 PGC2018-096540-B-I00 |
Cita | 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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