相关论文: Analytical solutions for Navier-Stokes equations w…

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 study existence, uniqueness and regularity properties of classical solutions to viscous Hamilton-Jacobi equations with Caputo time-fractional derivative. Our study relies on a combination of a gradient bound for the time-fractional…

We study spatial analyticity properties of solutions of the Navier-Stokes equations and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes…

With the previous results for the analytical blowup solutions of the N-dimensional Euler-Poisson equations, we extend the similar structure to construct an analytical family of solutions for the isothermal Navier-Stokes equations and…

We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…

We present a dimensionally split method for computing solutions to the compressible Navier-Stokes equations on Cartesian cut cell meshes. The method is globally second order accurate in the L1 norm, fully conservative, and allows the use of…

The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…

In this paper we present extensions of the schemes proposed in \cite{GM14} that lead to a decoupling of the velocity components in the momentum equation. The new schemes reduce the solution of the incompressible Navier-Stokes equations to a…

In this paper, the fractional-order Burgers-Poisson equation is introduced by replacing the first-order time derivative by fractional derivative of order $\alpha$. Both exact and approximate explicit solutions are obtained by employing…

The paper considers the time periodic problem of the Navier-Stokes system in an exterior domain under time periodic external forces. Existence of periodic mild solutions is obtained in the critical scale invariant space $C(\mathbb{R};L^n)$…

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and…

In this article, we systematically explain how to apply the analytical technique called the invariant subspace method to find various types of analytical solutions for a coupled nonlinear time-fractional system of partial differential…

This paper provides primarily an analytical ad hoc -solution for 3-dimensional, incompressible Navier-Stokes equations with a suitable external force field. The solution turns out to be smooth and integrable on the whole space. There is…

It is proved that there exists a local-in-time solution $u\in C([0,T),bmo(\mathbb{R}^d)^d)$ of the Navier-Stokes equations such that every $u(t)$ has an analytic extension on a complex domain whose size only depends on $t$ (and increases…

In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on…

The goal of the paper is to understand properties of the so-called ancient (backward) solutions to the Navier-Stokes equations. We focus on the case of the half space.

In this paper we present a method to derive classical solutions of the Navier-Stokes equations for non-stationary initial value problems in domain $\mathbb{R}^n$ ($n=2,3$ or higher). Exact solutions in $\mathbb{R}^2$ and $\mathbb{R}^3$ in…

In this paper, we establish the space-time analyticity of global solutions to the incompressible Navier-Stokes equations with small initial data in critical \emph{Besov} spaces $\dot B^{3/p-1}_{p,q}$. Time decay rates of higher order…

Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a rigorous framework to prove that solutions to the fractional Navier-Stokes equations, which involve the fractional Laplacian operator…

We present a general approach for obtaining the generalized transport equations with fractional derivatives using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev non-equilibrium…