Stochastic Tamed 3D Navier-Stokes Equations: Existence, Uniqueness and Ergodicity

In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and degenerated additive noise, using the notion of asymptotic strong Feller property proposed by Hairer and Mattingly \cite{Ha-Ma}, we prove the uniqueness of invariant measures for the corresponding transition semigroup.Comment: 38Pages, Correct some error

Cold Responsive \u3cem\u3eEARLI1\u3c/em\u3e Type HyPRPs Improve Freezing Survival of Yeast Cells and Form Higher Order Complexes in Plants

Plants have large families of proteins sharing a conserved eight-cysteine-motif (8CM) domain. The biological functions of these proteins are largely unknown. EARLI1 is a cold responsive Arabidopsis gene that encodes a hybrid proline-rich protein (HyPRP) with a three-domain architecture: a putative signal peptide at the N-terminus, a proline-rich domain (PRD) in the middle, and an 8CM domain at the C-terminus. We report here that yeast cells expressing different EARLI1 genes had significantly higher rates of freezing survival than empty-vector transformed controls. Arabidopsis plants with knocked down EARLI1 genes had an increased tendency for freezing-induced cellular damage. EARLI1-GFP Fluorescence in transgenic plants and immunoblot analyses using protoplasts suggested cell wall localization for EARLI1 proteins. Immunoblot analyses showed that EARLI1 proteins form higher order complexes in plants, and that the PRD is a soluble and the 8CM an insoluble protein domain. We propose that EARLI1 proteins have a bimodular architecture in which the PRD may interact with the cell wall and the 8CM domain with the plasma membrane to protect the cells during freezing stress