论文标题
部分可观测时空混沌系统的无模型预测
The critical variational setting for stochastic evolution equations
论文作者
论文摘要
在本文中，我们介绍了准或半线性类型的抛物线随机演化方程的关键变异设置。我们的结果改善了经典变异环境中的许多抽象结果。特别是，我们能够通过更灵活的本地Lipschitz条件来代替通常的弱或局部单调条件。此外，乘法噪声的通常生长条件大大削弱。我们的新环境提供了一般条件，在该条件下，本地和全球存在和独特性的存在。此外，我们证明了对初始数据的持续依赖性。我们表明，许多经典的变化设置无法涵盖的许多经典SPD确实适合关键变化环境。特别是，Cahn-Hilliard方程，驯服Navier-Stokes方程和Allen-Cahn方程就是这种情况。
In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. In addition, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn-Hilliard equation, tamed Navier-Stokes equations, and Allen-Cahn equation.
