The exponential stability for locally monotone stochastic partial differential equations

This paper mainly studies the exponential stability for a class of nonlinear stochastic partial differential equations with locally monotone coefficients. The generalized variational framework is adopted to analyze the mean square exponential stability and pathwise exponential stability. Additionally, the use of multiplicative Ito noise with sufficient strength to enhance the stability of solution to stochastic partial differential equation is explored when the mean square exponential stability does not hold.