论文标题
具有单调非线性的SPDE的高阶矩
Higher order moments for SPDE with monotone nonlinearities
论文作者
论文摘要
本文介绍了一种新的$ p $依赖性的强制性条件，通过该条件可以通过该条件在变化框架中的大型SPDE中获得解决方案的$ l^p $大事。如果$ p = 2 $，我们的状况将减少到经典的强制性条件，这仅能产生解决方案的第二瞬间。抽象结果表明是最佳的。此外，将结果应用于获得$ l^p $ - 用于几个经典SPDE的解决方案，例如带有dirichlet和neumann边界条件的随机热方程，汉堡方程以及两个空间维度的Navier-Stokes方程。此外，我们可以使用我们的统一的强制性条件来恢复SPDES和高阶SPDES系统的最新结果。
This paper introduces a new $p$-dependent coercivity condition through which $L^p$-moments for solutions can be obtained for a large class of SPDEs in the variational framework. If $p=2$, our condition reduces to the classically coercivity condition, which only yields second moments for the solution. The abstract result is shown to be optimal. Moreover, the results are applied to obtain $L^p$-moments of solutions for several classical SPDEs such as stochastic heat equations with Dirichlet and Neumann boundary conditions, Burgers' equation and the Navier-Stokes equations in two spatial dimensions. Furthermore, we can recover recent results for systems of SPDEs and higher order SPDEs using our unifying coercivity condition.
