Unique Measure for Time-Dependent Random Dynamical Systems
Gregory Varner
TL;DR
This paper establishes the uniqueness and exponential mixing of measures for the 2D Navier-Stokes equations with time-dependent forces, extending previous results to inhomogeneous Markov processes.
Contribution
It extends the uniqueness of measure results to time-inhomogeneous Markov processes for the 2D Navier-Stokes equations with random and deterministic forces.
Findings
Unique measure for 2D Navier-Stokes with time-dependent forces
Exponential mixing of the measures
Extension of homogeneous results to inhomogeneous case
Abstract
This paper proves the uniqueness of measure for the two-dimensional Navier-Stokes equations under a random kick-force and a time-dependent deterministic force. By extending a result for uniqueness of measure for time-homogeneous Markov processes to the time-inhomogeneous case, it is shown that the measures are exponentially mixing for the 2D Navier-Stokes equations on the sphere.
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Taxonomy
TopicsNavier-Stokes equation solutions · Stochastic processes and financial applications · Stability and Controllability of Differential Equations