相关论文: Campanato estimates for the generalized Stokes Sys…
We study the existence of regular solutions of the incompressible stationary Navier-Stokes equations in $n$-dimensional Euclidean space with a given bounded external force of compact support. In dimensions $n\le 5$, the existence of such…
In this work, we present some new Carleman inequalities for Stokes and Oseen equations with non-homogeneous boundary conditions. These estimates lead to log type stability inequalities for the problem of recovering the solution of the…
In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent…
We consider the phase-integral method applied to an arbitrary ordinary linear differential equation of the second-order and study how its symmetries affect the connection matrices associated with its general solution. We reduce the obtained…
In this paper we construct non-trivial solutions to the stationary Navier-Stokes equations on the two dimensional torus which lie in $\bigcap_{\epsilon \in (0,1)} L^{2-\epsilon}(\mathbb{T}^2) \cap \dot H^{-\epsilon}(\mathbb{T}^2)$. Due to…
We obtain the Kato square root estimate for second order elliptic operators in divergence form with mixed boundary conditions on an open and possibly unbounded set in $\mathbb{R}^d$ under two simple geometric conditions: The Dirichlet…
We examine the conditional regularity of the solutions of Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if positive part of the radial component of…
Let $\mathcal A$ be an elliptic tensor. A function $v\in L^1(I;LD_{div}(B))$ is a solution to the non-stationary $\mathcal A $-Stokes problem iff \begin{align}\label{abs} \int_Q v\cdot\partial_t\phi\,dx\,dt-\int_Q \mathcal…
A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very…
We consider a functional semilinear Rayleigh-Stokes equation involving fractional derivative. Our aim is to analyze some circumstances, in those the global solvability and some results on asymptotic behavior of solutions take place. By…
In this paper we study the long-time stability of the Cauchy one-leg theta-methods for the two-dimensional NavierStokes equations. We establish the uniform dissipativity in H^1, in the sense that the semi-discrete-in-time approximations…
We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in…
The existence, uniqueness and uniformly estimates for solutions of the parameter dependent abstract Navier-Stokes problem on half space are derived. In application the existence, uniqueness and uniformly L^{p} estimates for solution of the…
We investigate the initial-boundary value problem for the Stokes system in the half-space, within the framework of weighted Lebesgue spaces. Introducing a new weight function defined via a product of powers of distances from fixed points,…
We study the stationary Navier--Stokes equations in the whole plane with a compactly supported force term and with a prescribed constant spatial limit. Prior to this work, existence of solutions to this problem was only known under special…
Following the Gallavotti's conjecture, Stationary states of Navier-Stokes fluids are proposed to be described equivalently by alternative equations besides the NS equation itself. We propose a model system symmetric under time-reversal…
We provide spatial discretizations of nonlinear incompressible Navier-Stokes equations with inputs and outputs in the form of matrices ready to use in any numerical linear algebra package. We discuss the assembling of the system operators…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
We consider the wellposedness of the fractional Navier-Stokes as a generalization of the wellposedness result in Koch-Tataru's paper. An interesting remark is that our result does not contradict to the well-known ill-posedness result for…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…