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Exponential mixing of Vlasov equations under the effect of gravity and boundary.
- Source :
-
Journal of Differential Equations . Sep2023, Vol. 366, p645-742. 98p. - Publication Year :
- 2023
-
Abstract
- In this paper, we study exponentially fast mixing induced/enhanced by gravity and stochastic boundary in the kinetic theory of Vlasov equations. We consider the Vlasov equations with and without a vertical magnetic field inside a horizontally-periodic 3D half-space equipped with a non-isothermal diffusive reflection boundary condition of bounded continuous boundary temperature at the bottom. We construct both stationary solutions and global-in-time dynamical solutions in L ∞. We prove that moments of a dynamical fluctuation around the steady solutions decay exponentially fast in L ∞. As a key of this proof, we establish a uniform bound of so-called residual measures independently of the bouncing number of stochastic characteristics, by constructing a continuous stationary outgoing boundary flux which is strictly positive almost everywhere. [ABSTRACT FROM AUTHOR]
- Subjects :
- *VLASOV equation
*DIFFERENTIAL equations
*GRAVITY
*MAGNETIC fields
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 366
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 164109794
- Full Text :
- https://doi.org/10.1016/j.jde.2023.04.038