We provide an existence and uniqueness result for mild solutions to semilinear stochastic partial differential equations in the framework of semigroup approach with locally monotone coefficients. An important component proof is application dilation theorem Nagy, which allows us reduce problem infinite dimensional on a larger Hilbert space. Properties like Markov property are discussed as well.

In this paper, we show the optimal decay rate estimates of space-time derivatives and joint analyticity solutions to Navier-Stokes equations. As it is known from Hartogs's theorem, for a complex function with two variables, respect variables can be derived combining each variable. However, as real space time, equations cannot directly obtained combination time analyticity. Our result seems firs...