论文标题
部分可观测时空混沌系统的无模型预测
Wellposedness of nonlinear flows on manifolds of bounded geometry
论文作者
论文摘要
我们提供简单的条件，以确保强烈的椭圆运算符$ l $在限制几何形状的任意完整多种形态上在Hölder空间上产生分析性半群。这是通过确定$ l $是“部门”的等效属性来完成的，该条件指定了分解$（λi -l）^{ - 1} $的衰减为$λ$从$ l $的HölderSpectrum偏离。作为一个步骤，如果$λ$足够大，我们证明了这种分解的存在，并且在这类歧管上，使用半经典伪模分子的几何微局部版本。然后，我们获得的$ l $和$ e^{ - tl} $的属性可以用来证明广泛的非线性流量的良好性。我们通过证明与环境阻塞量张量相关的流量的hölder空间上的良好性来说明这一点。
We present simple conditions which ensure that a strongly elliptic operator $L$ generates an analytic semigroup on Hölder spaces on an arbitrary complete manifold of bounded geometry. This is done by establishing the equivalent property that $L$ is "sectorial", a condition that specifies the decay of the resolvent $(λI - L)^{-1}$ as $λ$ diverges from the Hölder spectrum of $L$. As one step, we prove existence of this resolvent if $λ$ is sufficiently large, and on this general class of manifolds, use a geometric microlocal version of the semiclassical pseudodifferential calculus. The properties of $L$ and $e^{-tL}$ we obtain can then be used to prove wellposedness of a wide class of nonlinear flows. We illustrate this by proving wellposedness on Hölder spaces of the flow associated to the ambient obstruction tensor on complete manifolds of bounded geometry.
