Related papers: Weak Solutions of stochastic recursions: an explic…

In this paper we prove the almost sure existence of global weak solution to the 3D incompressible Navier-Stokes Equation for a set of large data in $\dot{H}^{-\alpha}(\mathbb{R}^{3})$ or $\dot{H}^{-\alpha}(\mathbb{T}^{3})$ with…

In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. In…

In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…

We attempt to systematically derive perturbative quantum corrections to the Berry diagonal approximation of the two-level correlation function (TLCF) for chaotic systems. To this end, we develop a ``weak diagonal approximation'' based on a…

The paper is dedicated to studying the problem of Poisson stability (in particular stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, Bohr almost automorphy, Birkhoff recurrence, almost recurrence in the sense of…

We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative…

We prove strong rate resp. weak rate ${\mathcal O}(\tau)$ for a structure preserving temporal discretization (with $\tau$ the step size) of the stochastic Allen-Cahn equation with additive resp. multiplicative colored noise in $d=1,2,3$…

In this paper, we consider the fractional Navier-Stokes equations. We extend a previous non-uniqueness result due to Cheskidov and Luo, found in [5], from Navier-Stokes to the fractional case, and from $L^1$-in-time, $W^{1,q}$-in-space…

We introduce a notion of weak solution for abstract fractional differential equations, motivated by the definition of Caputo derivative. We prove existence results for weak and strong solutions. We also give two examples as application of…

We construct a martingale solution of the stochastic nonlinear Schr\"odinger equation with a multiplicative noise of jump type in the Marcus canonical form. The problem is formulated in a general framework that covers the subcritical…

We construct an efficient approach to deal with the global regularity estimates for a class of elliptic double-obstacle problems in Lorentz and Orlicz spaces. The motivation of this paper comes from the study on an abstract result in the…

We consider the (barotropic) Euler system describing the motion of a compressible inviscid fluid driven by a stochastic forcing. Adapting the method of convex integration we show that the initial value problem is ill-posed in the class of…

This note is an attempt to unconditionally prove the existence of weak one way functions (OWF). Starting from a provably intractable decision problem $L_D$ (whose existence is nonconstructively assured from the well-known discrete…

In this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ODE for the different phases of steel, and Maxwell's equations in a potential formulation. The existence of…

In this short paper, we present a simple variant of the recursive path ordering, specified for Logically Constrained Simply Typed Rewriting Systems (LCSTRSs). This is a method for curried systems, without lambda but with partially applied…

In this paper, we establish the well-posedness of Cauchy problems for weak solutions to second-order degenerate parabolic equations with a non-smooth, time-dependent degenerate elliptic part that includes both bounded and unbounded…

This article study the fractional Hamiltonian systems \begin{eqnarray}\label{00} {_{t}}D_{\infty}^{\alpha}({_{-\infty}}D_{t}^{\alpha}u) + \lambda L(t)u = \nabla W(t, u), \;\;t\in \mathbb{R}, \end{eqnarray} where $\alpha \in (1/2, 1)$,…

We study the regularity and well-posedness of the local, first-order forward-backward mean field games system, assuming a polynomially growing cost function and a Hamiltonian of quadratic growth. We consider systems and terminal data that…

This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…

We study stable solutions to fractional semilinear equations $(-\Delta)^s u = f(u)$ in $\Omega \subset \mathbb{R}^n$, for convex nonlinearities $f$, and under the Dirichlet exterior condition $u=g$ in $\mathbb{R}^n \setminus \Omega$ with…