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Well-posedness of stochastic partial differential equations with Lyapunov condition. (English) Zbl 1284.60130
Summary: We show the existence and uniqueness of strong solutions for a large class of SPDEs, where the coefficients satisfy the local monotonicity and Lyapunov condition (one-sided linear growth condition). Moreover, some new invariance result and stronger regularity estimate are also established for the solutions. As examples, the main result is applied to stochastic tamed 3D Navier-Stokes equations, stochastic generalized curve shortening flow, singular stochastic $$p$$-Laplace equations, stochastic fast diffusion equations, stochastic Burgers type equations and stochastic reaction-diffusion equations.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 37L30 Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents 34D45 Attractors of solutions to ordinary differential equations
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