相关论文: Regularization by rough Kraichnan noise for the ge…
In this paper we aim at generalizing the results of A. K. Zvonkin and A. Y. Veretennikov on the construction of unique strong solutions of stochastic differential equations with singular drift vector field and additive noise in the…
We establish the existence and uniqueness of pathwise strong solutions to the stochastic 3D primitive equations with only horizontal viscosity and diffusivity driven by transport noise on a cylindrical domain $M=(-h,0) \times G$, $G\subset…
We develop local discontinuous Galerkin (LDG) methods for conservation laws with heterogeneous stochastic fluxes, where the Stratonovich-driven transport terms may be linear or nonlinear. Such equations arise, for example, in simplified…
In this paper linear stochastic transport and continuity equations with drift in critical $L^{p}$ spaces are considered. In this situation noise prevents shocks for the transport equation and singularities in the density for the continuity…
We show the existence and uniqueness of strong solutions for stochastic differential equation driven by partial $\alpha$-stable noise and partial Brownian noise with singular coefficients. The proof is based on the regularity of degenerate…
In this paper, we establish existence and uniqueness of strong solutions for a stochastic differential equation driven by an additive noise given by the sum of two correlated fractional Brownian sheets with different Hurst parameters. Our…
We investigate a stochastic transport equation driven by a multiplicative noise. For $L^q(0,T;W^{1,p}({\mathbb R}^d;{\mathbb R}^d))$ drift coefficient and $W^{1,r}({\mathbb R}^d)$ initial data, we obtain the existence and uniqueness of…
In this paper, we study the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ for general parameter $\alpha\in(0,1)$ and multiplicative noise. We prove the existence of weak solutions and Markov selections for multiplicative noise…
We investigate the effects of the propagation of a non-degenerate Brownian noise through a chain of deterministic differential equations whose coefficients are rough and satisfy a weak like H{\"o}rmander structure (i.e. a non-degeneracy…
We study a model of the motion by mean curvature of an (1+1) dimensional interface in a 2D Brownian velocity field. For the well-posedness of the model we prove existence and uniqueness for certain degenerate nonlinear stochastic evolution…
In this paper, we establish the ergodicity of generalized Dean--Kawasaki equations with correlated noise and Dirichlet boundary conditions. In contrast to the ergodicity results of Fehrman, Gess, and Gvalani arXiv:2206.14789, our analysis…
A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative renormalization leads to convergence of the solutions of…
We study local existence and uniqueness for a surface growth model with space-time white noise in 2D. Unfortunately, the direct fixed-point argument for mild solutions fails here, as we do not have sufficient regularity for the stochastic…
We consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior. In particular, we focus on the case when the driving noise is a rough path valued fractional Brownian motion with…
In this paper we construct a new type of noise of fractional nature that has a strong regularizing effect on differential equations. We consider an equation with this noise with a highly irregular coefficient. We employ a new method to…
We consider a quasilinear parabolic stochastic partial differential equation driven by a multiplicative noise and study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine…
We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot-Savart kernel and the same…
The results of the author and Gess [27] develop a robust well-posedness theory for a broad class of conservative stochastic PDEs, with both probabilistically stationary and non-stationary Stratonovich noise, and with irregular noise…
In this paper, we investigate the Cauchy problem associated with the stochastic hyperbolic Keller-Segel (SHKS) equation featuring multiplicative noises on the torus $\mathbb{T}^d$. First, we establish the local existence and uniqueness of…
We study patch solutions of a family of transport equations given by a parameter $\alpha$, $0< \alpha <2$, with the cases $\alpha =0$ and $\alpha =1$ corresponding to the Euler and the surface quasi-geostrophic equations respectively. In…