论文标题
具有加性噪声的随机扩散表面准整形方程的能量解决方案的存在和独特性
Existence and Uniqueness of Energy Solutions to the Stochastic Diffusive Surface Quasi-Geostrophic Equation with Additive Noise
论文作者
论文摘要
我们继续研究几乎不粘附的周期性表面准地神性方程的动力学。在这里，我们考虑了形式\ begin {equation*} \ begin {cases}dθ_t + | d | d |^{2Δ}θ_t\，dx +（u_t \ cdot \ cdot \ nabla）θ_t\，dx + | d | d | d | d |^u__ |^u__t = 0 0 0 c. \ nabla^\ perp | d |^{ - 1}θ_t。 \ end {cases} \ end {等式*}我们构建了P. Goncalves和M. Jara（2014）引入的全局能量解决方案（2014年），任何$δ> 0 $，因此任何少量的扩散允许我们构建解决方案。此外，我们还表明，在足够高的扩散$δ> \ frac32 $的情况下，这些能量解决方案的路径唯一性保持。
We continue our study of the dynamics of a nearly inviscid periodic surface quasi-geostrophic equation. Here we consider a slightly diffusive stochastic SQG equation of the form \begin{equation*} \begin{cases} dθ_t + |D|^{2δ}θ_t\,dx + (u_t \cdot \nabla)θ_t\,dx + |D|^δdW_t = 0 \\ u_t = \nabla^\perp|D|^{-1}θ_t. \end{cases} \end{equation*} We construct global energy solutions as introduced by P. Goncalves and M. Jara (2014) for any $δ> 0$, so that any small amount of diffusion permits us to construct solutions. We show moreover that pathwise uniqueness of these energy solutions holds in the presence of sufficiently high diffusion $δ> \frac32$.
