On the 3D Navier-Stokes Equations with a Linear Multiplicative Noise and Prescribed Energy
Analysis of PDEs
2022-12-22 v1 Probability
Abstract
For a prescribed deterministic kinetic energy we use convex integration to construct analytically weak and probabilistically strong solutions to the 3D incompressible Navier-Stokes equations driven by a linear multiplicative stochastic forcing. These solutions are defined up to an arbitrarily large stopping time and have deterministic initial values, which are part of the construction. Moreover, by a suitable choice of different kinetic energies which coincide on an interval close to time 0, we obtain non-uniqueness.
Keywords
Cite
@article{arxiv.2212.11257,
title = {On the 3D Navier-Stokes Equations with a Linear Multiplicative Noise and Prescribed Energy},
author = {Stefanie Elisabeth Berkemeier},
journal= {arXiv preprint arXiv:2212.11257},
year = {2022}
}