具有小$H^{1/2}$初值的随机Navier-Stokes方程的几乎全局存在性
Almost global existence for the stochastic Navier-Stokes equations with small $H^{1/2}$ data
AI总结：
该文研究带乘性噪声的小$H^{1/2}$初值随机Navier-Stokes方程的解的全局存在性，证明了小初值小噪声下解以接近1的概率全局存在，非小噪声下在小区间上以接近1的概率全局存在。
摘要：
本文研究带乘性噪声、初值属于$H^{1/2}(\mathbb{T}^{3})$的随机Navier-Stokes方程的解的全局存在性。我们证明：若初值与噪声足够小，解以任意接近1的概率全局存在；若不假设噪声很小，解则在足够小的确定性时间区间上以任意接近1的概率全局存在。
英文摘要：
We address the global existence of solutions to the stochastic Navier-Stokes equations with multiplicative noise and with initial data in $H^{1/2}(\mathbb{T}^{3})$. We prove that the solution exists globally in time with probability arbitrarily close to~$1$ if the initial data and noise are sufficiently small. If the noise is not assumed to be small, then the solution is global on a sufficiently small deterministic time interval with probability arbitrarily close to~$1$.
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