相关论文: Local and global well-posedness of 2d periodic mul…

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 study well-posedness of viscous nonlinear wave equations (vNLW) on the two-dimensional torus with a stochastic forcing. In particular, we prove pathwise global well-posedness of the stochastic defocusing vNLW with an additive stochastic…

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 consider the nonlinear Schr\"odinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced…

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, the local wellposedness of a general Gross-Pitaevskii equation with rough potential is proven in dimension 2. The class of rough potentials we are considering is large enough to contain the spatial white noise and thus a…

Thanks to an approach inspired from Burq-Lebeau \cite{bule}, we prove stochastic versions of Strichartz estimates for Schr\"odinger with harmonic potential. As a consequence, we show that the nonlinear Schr\"odinger equation with quadratic…

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 consider the nonlinear Schr\"odinger equation on the $d$-dimensional torus $\mathbb T^d$, with the nonlinearity of polynomial type $|u|^{2\sigma}u$. For any $\sigma \in \mathbb N$ and $s>\frac d2$ we prove that adding to this equation a…

We study the nonlinear Schr\"odinger equation (NLS) with the quadratic nonlinearity $|u|^2$, posed on the two-dimensional torus $\mathbb{T}^2$. While the relevant $L^3$-Strichartz estimate is known only with a derivative loss, we prove…

We consider the defocusing periodic fractional nonlinear Schr\"odinger equation $$ i \partial_t u +\left(-\Delta\right)^{\alpha}u=-\lvert u \rvert ^2 u, $$ where $\frac{1}{2}< \alpha < 1$ and the operator $(-\Delta)^\alpha$ is the…

We continue our study for the stochastic defocusing mass crtical nonlinear Schr\"odinger equation with conservative multiplicative noise, and show that it is globally well-posed for arbitrary initial data in $L_{\omega}^{\infty}L_{x}^{2}$.…

We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on [14], where Mourrat and Weber showed the global well-posedness for the…

In this paper, we are concerned with the local and global existence for the stochastic Prandtl equation in two and three dimensions, which governs the velocity field inside the boundary layer that appears in the inviscid limit of the…

We study the stochastic Nonlinear Schr\"{o}dinger system with multiplicative white noise in energy space $H^1$. Based on deterministic and stochastic Strichartz estimates, we prove the local well-posedness and uniqueness of mild solution.…

We consider the long time well-posedness of the Cauchy problem with large Sobolev data for a class of nonlinear Schr\"odinger equations (NLS) on $\mathbb{R}^2$ with power nonlinearities of arbitrary odd degree. Specifically, the method in…

This paper investigates the local and global well-posedness for the inhomogeneous nonlinear Schr\"{o}dinger (INLS) equation $iu_{t} +\Delta u=\lambda \left|x\right|^{-b} \left|u\right|^{\sigma } u, u(0)=u_{0} \in L^{2}(\mathbb R^{n})$,…

The optimal $L^4$-Strichartz estimate for the Schr{\"o}dinger equation on the two-dimensional rational torus $\mathbb{T}^2$ is proved, which improves an estimate of Bourgain. A new method based on incidence geometry is used. The approach…

In this work, we consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation in $\mathbb{R}^n$ \begin{align} i\partial_t u + \Delta u + \gamma |x|^{-b}|u|^{\alpha} u = 0, \end{align} where $\gamma=\pm 1$, and $\alpha$ and $b$ are…

We investigate the global well-posedness and ergodicity of the complex Ginzburg-Landau equation with a general nonlinear term on the two-dimensional torus, driven by complex-valued space-time white noise. Due to the roughness of noise, the…