论文标题
随机2D流体动力学系统的适应性，带有乘法lévy噪声
Well-posedness of Stochastic 2D Hydrodynamics type Systems with Multiplicative Lévy Noises
论文作者
论文摘要
我们确定了由Lévy类型的乘法噪声驱动的抽象非线性方程的解决方案的存在和唯一性，该方程涵盖了许多流体动力学模型，包括2D Navier-Stokes方程，2D MHD方程，2D MHD方程，2D磁性Bernard问题，以及几种湍流模型。在现有有关该主题的文献中，除了经典的Lipschitz和单方面的线性生长条件外，其他假设（可能是毫不典型的假设）也需要在随机扰动的系数上。本文是为了摆脱这些朴素的假设。我们对随机扰动系数的假设即使对于Wiener案例也是新的，并且从某种意义上说，它被证明很清晰。新的削减论点和能量估计程序在确定该假设下的存在和独特性方面起着重要作用。
We establish the existence and uniqueness of solutions to an abstract nonlinear equation driven by a multiplicative noise of Lévy type, which covers many hydrodynamical models including 2D Navier-Stokes equations, 2D MHD equations, the 2D Magnetic Bernard problem, and several Shell models of turbulence. In the existing literature on this topic, besides the classical Lipschitz and one sided linear growth conditions, other assumptions, which might be untypical, are also required on the coefficients of the stochastic perturbations. This paper is to get rid of these untypical assumptions. Our assumption on the coefficients of stochastic perturbations is new even for the Wiener cases, and in some sense, is shown to be quite sharp. A new cutting-off argument and energy estimation procedure play an important role in establishing the existence and uniqueness under this assumption.
