相关论文: Temporal regularity of symmetric stochastic $p$-St…
This paper investigates the pathwise uniform convergence in probability of fully discrete finite-element approximations for the two-dimensional stochastic Navier-Stokes equations with multiplicative noise, subject to no-slip boundary…
We consider local weak solutions to the widely degenerate parabolic PDE \[ \partial_{t}u-\mathrm{div}\left((\vert Du\vert-\lambda)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f\qquad\mathrm{in}\ \ \Omega_{T}=\Omega\times(0,T), \] where…
We consider the steady Stokes equations supplemented with Navier boundary conditions including a non-negative friction coefficient. We prove maximal regularity estimates (including the prominent spaces $W^{1,p}$ and $W^{2,p}$ for…
We present an $L_{p}$-theory ($p\geq 2$) for time-fractional stochastic partial differential equations driven by L\'evy processes of the type $$ \partial^{\alpha}_{t}u=\sum_{i,j=1}^d a^{ij}u_{x^{i}x^{j}}…
We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
We theoretically investigate the time dependence of the first order coherence function for a one-dimensional driven dissipative non-equilibrium condensate. Simulations on the generalized Gross-Pitaevskii equation (GGPE) show that the…
We consider a class of parabolic variational inequalities with time dependent obstacle of the form $|{\boldsymbol u}(x,t)| \le p(x,t)$, where ${\boldsymbol u}$ is the velocity field of a fluid governed by the Navier--Stokes variational…
In this paper, we establish the strong($H^1$) well-posedness of the two dimensional stochastic Navier-Stokes equation with multiplicative noise on moving domains. Due to the nonlocality effect, this equation exhibits a ``piecewise"…
A right continuous Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier-Stokes equation, and we call such stochastic system as stochastic Navier-Stokes equation with Markov switching. In the present…
We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $O \subset R^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of…
We study the time-dependent Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion, and…
In this article, we consider non-smooth time-dependent domains and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic…
We study the stationary Stokes system in divergence form. The coefficients are assumed to be merely measurable in one direction and have Dini mean oscillations in the other directions. We prove that if $(u,p)$ is a weak solution of the…
We study the nonlinear localized modes in two-component Bose-Einstein condensates with parity-time-symmetric Scarf-II potential, which can be described by the coupled Gross-Pitaevskii equations. Firstly, we investigate the linear stability…
We consider the 3D incompressible hypodissipative Navier-Stokes equations, when the dissipation is given as a fractional Laplacian $(-\Delta )^s$ for $s\in (\frac34,1)$, and we provide a new bootstrapping scheme that makes it possible to…
We study the stationary Stokes system with Dini mean oscillation coefficients in a domain having $C^{1,\rm{Dini}}$ boundary. We prove that if $(u, p)$ is a weak solution of the system with zero Dirichlet boundary condition, then $(Du,p)$ is…
We consider stationary solutions of the three dimensional Navier--Stokes equations (NS3D) with periodic boundary conditions and driven by an external force which might have a deterministic and a random part. The random part of the force is…
Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the unique strong solvability of time-inhomogeneous stochastic differential equations with drift coefficients in critical Lebesgue spaces,…
We establish well-posedness results for multidimensional non degenerate $\alpha$-stable driven SDEs with time inhomogeneous singular drifts in $\mathbb{L}^r-{\mathbb B}_{p,q}^{-1+\gamma}$ with $\gamma<1$ and $\alpha$ in $(1,2]$, where…