A Lower Bound Estimate of Life Span of Solutions to Stochastic 3D Navier-Stokes Equations with Convolution Type Noise

Abstract

In this paper we investigate the stochastic 3D Navier-Stokes equations perturbed by linear multiplicative Gaussian noise of convolution type by transformation to random PDEs. We are not interested in the regularity of the initial data. We focus on obtaining bounds from below for the life span associated with regular initial data. The key point of the proof is the fixed point argument.