Well‐posedness of time‐space fractional stochastic evolution equations driven by α‐stable noise

Abstract

This paper is devoted to the well‐posedness for time‐space fractional Ginzburg‐Landau equation and time‐space fractional Navier‐Stokes equations by α‐stable noise. The spatial regularity and the temporal regularity of the nonlocal stochastic convolution are firstly established, and then the existence and uniqueness of the global mild solution are obtained by the Banach fixed point theorem and Mittag‐Leffler functions, respectively. Numerical simulations for time‐space fractional Ginzburg‐Landau equation are provided to verify the analysis results.

Upper semi-continuity of random attractors and existence of invariant measures for nonlocal stochastic Swift-Hohenberg equation with multiplicative noise

“…Due to the delicate impact on the deterministic cases, increasing concern of the randomness has occurred all over the development of evolution systems (e.g. [8,10,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]) in recent decades. It becomes centrally significant to take stochastic effects into account for mathematical models of complex phenomena in engineering and science.…”