Related papers: The stochastic $p$-Laplace equation on $\mathbb{R}…
We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations…
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L^p$ spaces on bounded domains of $\mathbb{R}^n$ with a nonlinear drift term given by the superposition operator generated by a…
We study the wellposedness and pathwise regularity of semilinear non-autonomous parabolic evolution equations with boundary and interior noise in an $L^p$ setting. We obtain existence and uniqueness of mild and weak solutions. The boundary…
We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a very general nonlinear multiplicative noise. In the two-dimensional case we…
We consider stochastic partial differential equations on $\mathbb{R}^{d}, d\geq 1$, driven by a Gaussian noise white in time and colored in space, for which the pathwise uniqueness holds. By using the Skorokhod representation theorem we…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous…
The stochastic $p$-Laplace equation with multiplicative transport noise is studied on the torus $\mathbb T^d\, (d\geq 2)$. It is shown that the dissipation is enhanced by transport noise in both the averaged sense and the pathwise sense.
We establish the first existence and uniqueness result for mild solutions of abstract stochastic evolution equations driven by arbitrary cylindrical L\'evy processes in Hilbert spaces. The coefficients are assumed to satisfy global…
We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time.…
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L_p$ spaces, driven by multiplicative Wiener noise, with a drift term given by an evaluation operator that is assumed to be…
One-dimensional stochastic differential equations with additive L\'evy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a L\'evy symmetric stable process with…
We consider the natural time-dependent fractional $p$-Laplacian equation posed in the whole Euclidean space, with parameters $p>2$ and $s\in (0,1)$ (fractional exponent). We show that the Cauchy Problem for data in the Lebesgue $L^q$ spaces…
Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $\sigma$-finite intensity…
The present article is devoted to well-posedness by noise for the continuity equation. Namely, we consider the continuity equation with non-linear and partially degenerate stochastic perturbations in divergence form. We prove the existence…
We study the well solvability of nonlinear backward stochastic evolutionary equations driven by a space-time white noise. We first establish a novel a priori estimate for solution of linear backward stochastic evolutionary equations, and…
We propose and study a temporal, and spatio-temporal discretisation of the 2D stochastic Navier--Stokes equations in bounded domains supplemented with no-slip boundary conditions. Considering additive noise, we base its construction on the…
Considering the stochastic Navier-Stokes system in $\mathbb{R}^d$ forced by a multiplicative white noise, we establish the local existence and uniqueness of the strong solution when the initial data take values in the critical space…
In this paper, we prove existence, uniqueness and regularity for a class of stochastic partial differential equations with a fractional Laplacian driven by a space-time white noise in dimension one. The equation we consider may also include…
In this work, we investigate the well-posedness of a stochastic heat equation with an arbitrary (but polynomial) nonlinearity in any dimension $d\geq 1$ perturbed by a multiplicative white noise in the Stratonovich form, subject to an…