Related papers: Rigorous bounds of Stokes constants for some nonli…
In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…
Higher order moment estimates for solutions to nonlinear SPDEs governed by locally-monotone operators are obtained under appropriate coercivity condition. These are then used to extend known existence and uniqueness results for nonlinear…
We prove some bounds for the eigenfunctions of the Stokes problem under Navier boundary conditions in a cube.
We study the Hardy inequality when the singularity is placed on the boundary of a bounded domain in $\mathbb{R}^n$ that satisfies both an interior and exterior ball condition at the singularity. We obtain the sharp Hardy constant $n^2/4$ in…
In this paper we study the local behavior of a solution to the Stokes system with singular coefficients. One of the main results is the bound on the vanishing order of a nontrivial solution to the Stokes system, which is a quantitative…
We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous work for the case of one singularity, and illustrates the…
The completeness of solutions of homogeneous as well as non-homogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes…
In this paper, we study the regularity problem of the 3D incompressible Navier\~nStokes equations. We prove that the strong solution exists globally for new regularity criteria. For negligible forces, we give an improvement of the known…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has appeared in many physical applications, from acoustic and…
We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of…
We prove the local boundedness for solutions to a class of obstacle problems with non-standard growth conditions. The novelty here is that we are able to establish the local boundedness under a sharp bound on the gap between the growth…
We consider nonstationary Stokes equations in nondivergence form with variable viscosity coefficients and generalized Navier slip boundary conditions with slip tensor $\mathcal{A}$ in a domain $\Omega$ in $\mathbb{R}^d$. First, under the…
The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…
We discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms.
We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain…
The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), nonstandard finite difference schemes are in common use for…