论文标题
带有运输噪音的大湖方程的本地良好性
Local well-posedness for the great lake equation with transport noise
论文作者
论文摘要
这项工作是作者在由运输型噪声驱动的随机2D Euler方程中的作品的延续。在这里，我们取消了不可压缩的限制。相反，我们假设加权不可压缩条件。这种情况的灵感来自于具有自由上表面和空间变化的底部形状的盆地中流体的物理模型。此外，我们假设涡度函数运算符的一种不同形式的涡度操作员概括了出现在Euler方程中的标准生物射击操作员。这两种特性在称为大湖方程的物理模型中展出。因此，我们将本文分析的模型称为随机大湖方程。流函数运算符的新涡度概括了卷曲操作员，并显示出良好的规律性属性。我们还表明，保留了溶液的初始平滑度。这些论点是基于构建粘性解决方案家族的，该粘性解决方案被证明是相对紧凑的，并收敛到原始方程的截断版本。最后，我们表明截断可以将其拆除至积极的停止时间。
This work is a continuation of the authors' work for the stochastic 2D Euler equation driven by transport type noise. Here we lift the incompressibility constraint. Instead we assume a weighted incompressibility condition. This condition is inspired by a physical model for a fluid in a basin with a free upper surface and a spatially varying bottom topography. Moreover, we assume a different form of the vorticity to stream function operator that generalizes the standard Biot-Savart operator which appears in the Euler equation. These two properties are exhibited in the physical model called the great lake equation. For this reason we refer to the model analysed in this paper as the stochastic great lake equation. The new vorticity to stream function operator generalizes the curl operator and it is shown to have good regularity properties. We also show that the initial smoothness of the solution is preserved. The arguments are based on constructing a family of viscous solutions which is proved to be relatively compact and to converge to a truncated version of the original equation. Finally, we show that the truncation can be removed up to a positive stopping time.
