论文标题
Keller-Segel-Dean-Kawasaki动力学的添加剂近似值：paraconollollroll solutions的局部适应性
An Additive-Noise Approximation to Keller-Segel-Dean-Kawasaki Dynamics: Local Well-Posedness of Paracontrolled Solutions
论文作者
论文摘要
使用副控制分布的方法，我们显示了二维圆环Keller-Segel模型的波动流体动力学的添加噪声近似的局部良好性。我们的近似值是一种非线性的，非本地的，抛物线的随机PDE，具有不规则的，异质的时空噪声。由于不规则性和异质性，该方程式的解决方案必须通过一系列不同的场进行重归于。使用椭圆绿色功能的对称性（在我们的非本地术语中出现），我们确定重态化最大程度地分歧在对数上，对幂计数所期望的线性差异的改善。类似的取消也有助于减少反对差异的数量。
Using the method of paracontrolled distributions, we show the local well-posedness of an additive noise approximation to the fluctuating hydrodynamics of the Keller-Segel model on the two-dimensional torus. Our approximation is a non-linear, non-local, parabolic-elliptic stochastic PDE with an irregular, heterogeneous space-time noise. As a consequence of the irregularity and heterogeneity, solutions to this equation must be renormalised by a sequence of diverging fields. Using the symmetry of the elliptic Green's function, which appears in our non-local term, we establish that the renormalisation diverges at most logarithmically, an improvement over the linear divergence one would expect by power counting. Similar cancellations also serve to reduce the number of diverging counterterms.
