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

被引：0
作者：
Stefanie Elisabeth Berkemeier
机构：
[1] University of Bielefeld,Faculty of Mathematics
来源：
Journal of Evolution Equations | 2023年 / 23卷
关键词：
Stochastic Navier–Stokes equations; Multiplicative noise; Kinetic energy; Analytically weak solutions; Probabilistically strong solutions; Non-uniqueness; Convex integration;
D O I：
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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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