Related papers: Vector-valued stochastic delay equations - a weak …

We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function--valued…

Building on results obtained in [GVRS], we prove Local Stable and Unstable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rough paths theory and a semi-invertible Multiplicative Ergodic…

We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two…

We consider notions of weak solutions to a general class of parabolic problems of linear growth, formulated independently of time regularity. Equivalence with variational solutions is established using a stability result for weak solutions.…

In this work we prove uniqueness of distributional solutions to $2D$ Navier-Stokes equations in vorticity form $u_t-\nu\Delta u+ div (K(u)u)=0$ on $(0,\infty)\times\mathbb{R}^2$ with Radon measures as initial data, where $K$ is the…

The primitive equations for geophysical flows are studied under the influence of {\em stochastic wind driven boundary conditions} modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary…

We prove energy estimates for linear $p$-evolution equations in weighted Sobolev spaces under suitable assumptions on the behavior at infinity of the coefficients with respect to the space variables. As a consequence we obtain well…

We study the existence of weak solutions to the $p$-Navier-Stokes equations with a symmetric $p$-Laplacian on bounded domains. We construct a particular Schauder basis in $W_0^{1,p}(\Omega)$ with divergence free constraint and prove…

In this note we consider a class of neutral stochastic functional differential equations with finite delay driven simultaneously by a fractional Brownian motion and a Poisson point processes in a Hilbert space. We prove an existence and…

In this paper, we study well-posedness and exponential stability for semilinear second order evolution equations with memory and time-varying delay feedback. The time delay function is assumed to be continuous and bounded. Under a suitable…

In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under the suitable conditions.…

Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…

We study the Cauchy problem for $p$-adic nonlinear evolutionary pseudo-differential equations for complex-valued functions of a real positive time variable and p-adic spatial variables. Among the equations under consideration there is the…

We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…

The existence of global martingale weak solution for the 2D and 3D stochastic Cahn-Hilliard-Navier-Stokes equations driven by multiplicative noise in a smooth bounded domain is established. In particular, the system is supplied with the…

We investigate an evolutive system of non-linear partial differential equations derived from Oldroyd models on Non-Newtonian flows. We prove global existence of weak solutions, in the case of a smooth bounded domain, for general initial…

We consider a class of space-time coupled evolution equations (CEEs), obtained by a subordination of the heat operator. Our CEEs reformulate and extend known governing equations of non-Markovian processes arising as scaling limits of…

Discrete latent space models have recently achieved performance on par with their continuous counterparts in deep variational inference. While they still face various implementation challenges, these models offer the opportunity for a…

The weak solution to the Navier-Stokes equations in a bounded domain $D \subset \mathbb{R}^3$ with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all $t \geq 0$. In a…

We prove an existence and uniqueness result for the infinitely delayed stochastic evolution equation $$dU(t) = &\big(AU(t) + F(t,U_t)\big) dt + B(t,U_t)dW_H(t), t\in[0,T_0]$$ where $A$ is the generator of an analytic semigroup on a UMD…