• Corpus ID: 239024447

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

@inproceedings{Liang2021ALB,
title={A Lower Bound Estimate of Life Span of Solutions to Stochastic 3D Navier-Stokes Equations with Convolution Type Noise},
author={Siyu Liang},
year={2021}
}
• Siyu Liang
• Published 19 October 2021
• Mathematics
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.

## References

SHOWING 1-9 OF 9 REFERENCES
A nonlinear estimate of the life span of solutions of the three dimensional Navier–Stokes equations
• Mathematics
Tunisian Journal of Mathematics
• 2019
The purpose of this article is to establish bounds from below for the life span of regular solutions to the incompressible Navier-Stokes system, which involve norms not only of the initial data, but
Remark on the Lifespan of Solutions to 3-D Anisotropic Navier Stokes Equations
• Siyu Liang
• Physics
Communications in Mathematical Research
• 2020
The goal of this article is to provide a lower bound for the lifespan of smooth solutions to 3-D anisotropic incompressible Navier-Stokes system, which in particular extends a similar type of result
A remark on global solutions to random 3D vorticity equations for small initial data
• Mathematics
Discrete & Continuous Dynamical Systems - B
• 2019
In this paper, we prove that the solution constructed in \cite{BR16} satisfies the stochastic vorticity equations with the stochastic integration being understood in the sense of the integration of
Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions
• Mathematics
Journal of Evolution Equations
• 2019
The aim of this work is to prove an existence and uniqueness result of Kato–Fujita type for the Navier–Stokes equations, in vorticity form, in 2 D and 3 D , perturbed by a gradient-type
Fourier Analysis and Nonlinear Partial Differential Equations
• Mathematics
• 2011
Preface.- 1. Basic analysis.- 2. Littlewood-Paley theory.- 3. Transport and transport-diffusion equations.- 4. Quasilinear symmetric systems.- 5. Incompressible Navier-Stokes system.- 6. Anisotropic
About the behavior of regular Navier-Stokes solutions near the blow up
In this paper, we present some results about blow up of regular solutions to the homogeneous incompressible Navier-Stokes system, in the case of data in the Sobolev space $\dot{H}^{s}(\mathbb{R}^3)$,
Röckner, Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions
• Journal of Evolution Equations,
• 2020
Lemarié-Rieusset, Recent developments in the Navier–Stokes
• 2002