相关论文: Global well-posedness of the two-dimensional stoch…
We study the stochastic viscous nonlinear wave equations (SvNLW) on $\mathbb T^2$, forced by a fractional derivative of the space-time white noise $\xi$. In particular, we consider SvNLW with the singular additive forcing $D^\frac{1}{2}\xi$…
We study the two-dimensional stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing. In particular, we introduce a time-dependent renor- malization and prove that SNLW is pathwise locally well-posed. As…
We study the two-dimensional wave equation with cubic nonlinearity posed on $\mathbb R^2$, with space-time white noise forcing. After a suitable renormalisation of the nonlinearity, we prove global well-posedness for this equation for…
We study global-in-time dynamics of the stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing, posed on the two-dimensional torus. Our goal in this paper is two-fold. (i) By introducing a hybrid…
The aim of this paper is to prove, under minimum assumptions, the global well-posedness of the two-dimensional stochastic complex Ginzburg-Landau equation on the torus driven by the additive space-time white noise. In addition to the global…
We use Strichartz estimates with rough potentials like the spatial white noise on the 2 \ dimensional torus to prove global well-posedness of the multiplicative stochastic NLS with general integer powers in both the energy and strong regime…
We study global-in-time dynamics of the stochastic nonlinear beam equations (SNLB) with an additive space-time white noise, posed on the four-dimensional torus. The roughness of the noise leads us to introducing a time-dependent…
We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on $\mathbb{R}^{d}$ and $\mathbb{T}^{d}$ with $d \geq 3$. By adapting the probabilistic…
We study the stochastic complex Ginzburg-Landau equation (SCGL) with an additive space-time white noise forcing on the two-dimensional torus. This equation is singular and thus we need to renormalize the nonlinearity in order to give proper…
We study the stochastic cubic nonlinear wave equation (SNLW) with an additive noise on the three-dimensional torus $\mathbb{T}^3$. In particular, we prove local well-posedness of the (renormalized) SNLW when the noise is almost a space-time…
We study the singular stochastic wave equation on $\mathbb T^2$, with a cubic nonlinearity and Gaussian rough Mat\'ern forcing (a Fourier multiplier of order $\alpha>0$ applied to space-time white noise) and establish local well-posedness…
We consider the stochastic nonlinear Schr\"odinger equations (SNLS) posed on $d$-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness…
In this paper, we establish the strong($H^1$) well-posedness of the two dimensional stochastic Navier-Stokes equation with multiplicative noise on moving domains. Due to the nonlocality effect, this equation exhibits a ``piecewise"…
We first introduce a new model for a two-dimensional gauge-covariant wave equation with space-time white noise. In our main theorem, we obtain the probabilistic global well-posedness of this model in the Lorenz gauge. Furthermore, we prove…
We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schr\"odinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt the atomic spaces framework in the context of the…
We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid-structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane. The focus is on…
We study the two-dimensional stochastic nonlinear wave equation (SNLW) and stochastic nonlinear heat equation (SNLH) with a quadratic nonlinearity, forced by a fractional derivative (of order $\alpha > 0$) of a space-time white noise. In…
In this note, we establish a bi-parameter linear localization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing.
We consider the Cauchy problem for the stochastic Hartree nonlinear wave equations (SHNLW) with a cubic convolution nonlinearity and an additive stochastic forcing on the Euclidean space. Our goal in this paper is two-fold. (i) We study the…
In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the $d$-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g. the Allen-Cahn…