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math.AP2026
Almost sure spatial decay and almost sure nonlinear smoothing of some stochastic dispersive equations
Xiangqian Yan, Yongsheng Li, Jianhua Huang +1
In this paper, we consider the almost sure nonlinear smoothing, the almost sure spatial decay and the almost sure uniform convergence of the stochastic mKdV equation and the stocha…
math.PR2026
Well-posedness, mean attractors and invariant measures of stochastic discrete long-wave-short-wave resonance equations driven by locally Lipschitz nonlinear noise
Xia Pan, Jianhua Huang, Juntao Wu +1
This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: …
math.AP2026
The Cauchy problem for the generalized KdV equation in the Sobolev space
Xiangqian Yan, Yongsheng Li, Juan Huang +2
In this paper, we are concerned with the Cauchy problem for the generalized KdV equation with random data and rough data. Firstly, when , by using the initial value…