On the 3D Navier-Stokes equations with a linear multiplicative noise and prescribed energy

被引：2
作者：
Berkemeier, Stefanie Elisabeth [1 ]
机构：
[1] Univ Bielefeld, Fac Math, D-33501 Bielefeld, Germany
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2023年 / 23卷 / 02期
基金：
欧洲研究理事会;
关键词：
Stochastic Navier-Stokes equations; Multiplicative noise; Kinetic energy; Analytically weak solutions; Probabilistically strong solutions; Non-uniqueness; Convex integration; EULER; POSEDNESS;
D O I：
10.1007/s00028-023-00884-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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