论文标题
在3D Navier-Stokes方程中，具有线性乘法噪声和规定的能量
On the 3D Navier-Stokes Equations with a Linear Multiplicative Noise and Prescribed Energy
论文作者
论文摘要
对于规定的确定性动能，我们使用凸积分来构建由线性乘法随机强迫驱动的3D不可压缩的Navier-Stokes方程的分析性弱和概率强的解。这些解决方案的定义为任意的停止时间，并具有确定性的初始值，这是构造的一部分。此外，通过在接近时间0的间隔中重合的不同动能能量的适当选择，我们获得了非唯一性。
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.
