Related papers: Global Lipschitz stability for an inverse source p…

For two dimensional inhomogeneous Navier-Stokes of incompressible flows, with the assumption that the viscosity depends on the density but with a positive lower bound, using a partial regularity approach, in particular some enhanced decay…

A global time-discretized scheme for the Navier-Stokes equation system in its Leray projection form is defined. It is shown that the scheme converges to a bounded global classical solution for smooth data which have polynomial decay at…

For the N>=2 dimensional incompressible Naver-Stokes Equation, We have got its solution as a power series of time t, in which the coefficients are all known functions determined only by the initial velocity v0. We also prove that the…

Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we…

We here aim at proving the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where the initial density is discontinuous and the initial velocity has critical regularity.…

We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…

We prove that the steady incompressible Navier-Stokes equations with any given $(-3)$-homogeneous, locally Lipschitz external force on $\mathbb{R}^n\setminus\{0\}$, $4\leq n\leq 16$, have at least one $(-1)$-homogeneous solution which is…

In this lecture note, we study free boundary problems for the Navier-Stokes equations with and without surface tension. The local well-posedness, the global well-posedness, and asymptotics of solutions as time goes to infinity are studied…

We study the Navier-Stokes equations with transport noise in critical function spaces. Assuming the initial data belongs to $H^{1/2}$ almost surely, we establish the existence and uniqueness of a local-in-time probabilistically strong…

In this paper we prove a theorem of global time-extension for the local classical solution of Navier-Stokes's evolution problem in $\Real^n$ with $n\geqslant2$ for incompressible fluids subjected to external forces and regular initial…

In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The…

In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first…

We establish the global-in-time well-posedness of the two-dimensional incompressible Navier-Stokes equations with freely transported viscosity coefficient, under a scaling-invariant smallness condition on the initial data. The viscosity…

The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…

We prove existence of global regular axially-symmetric solutions to the Navier-Stokes equations in a cylindrical domain. We assume the periodic boundary conditions on the top and the bottom of the cylinder, but on the lateral part we assume…

We obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of data allowing growth at spatial infinity. Namely, we show the global existence of suitable weak solutions when the initial data…

In this paper, we prove the global well-posedness for the 3D rotating Navier-Stokes equations in the critical functional framework. Especially, this result allows to construct global solutions for a class of highly oscillating initial data.

We consider an anisotropic hyperbolic equation with memory term: $$ \partial_t^2 u(x,t) = \sum_{i,j=1}^n \partial_i(a_{ij}(x)\partial_ju) + \int^t_0 \sum_{| \alpha| \le 2} b_{\alpha}(x,t,\eta)\partial_x^{\alpha}u(x,\eta) d\eta + F(x,t) $$…

This paper is concerned with geometric regularity criteria for the Navier-Stokes equations in $\mathbb{R}^3_{+}\times (0,T)$ with no-slip boundary condition, with the assumption that the solution satisfies the `ODE blow-up rate' Type I…

We investigate in this paper the global stability of the compressible viscous surface waves in the absence of surface tension effect with a steady-state violating Rayleigh-Taylor instability and the reference domain being the horizontal…