Stochastic inviscid Leray-$α$ model with transport noise: convergence rates and CLT

Abstract

We consider the stochastic inviscid Leray-α model on the torus driven by transport noise. Under a suitable scaling of the noise, we prove that the weak solutions converge, in some negative Sobolev spaces, to the unique solution of the deterministic viscous Leray-α model. This implies that transport noise regularizes the inviscid Leray-α model so that it enjoys approximate weak uniqueness. Interpreting such limit result as a law of large numbers, we study the underlying central limit theorem and provide an explicit convergence rate.

LDP and CLT for SPDEs with transport noise

“…2.4 and 3.3). In fact, after the completion of this work, similar ideas and techniques were applied in [72,74] to derive such results for other equations of interest, respectively dyadic and Leray-α models.…”