相关论文: Finite time blow up for a Navier-Stokes like equat…

This paper addresses several problems associated to local energy solutions (in the sense of Lemari\'e-Rieusset) to the Navier-Stokes equations with initial data which is sufficiently small at large or small scales as measured using…

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 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…

In this paper, we study some conditions related to the question of the possible blow-up of regular solutions to the 3D Navier-Stokes equations. In particular, up to a modification in a proof of a very recent result from \cite{Isab}, we…

This note introduces a novel numerical analysis framework for the incompressible Navier-Stokes equations based on Besov spaces. The key contribution of this note is to establish the stability and convergence of a semi-implicit time-stepping…

We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on $R^3$. We show that there exists an open set in the space of 10-parameter families of initial conditions such that for each…

We consider the Cauchy problem for the full compressible Navier-Stokes equations with vanishing of density at infinity in R3. Our main purpose is to prove the existence (and uniqueness) of global strong and classical solutions and study the…

We prove that the Cauchy problem for the three dimensional Navier-Stokes equations is ill posed in $\dot{B}^{-1,\infty}_{\infty}$ in the sense that a ``norm inflation'' happens in finite time. More precisely, we show that initial data in…

We consider the stochastic Navier-Stokes equations with multiplicative noise with critical initial data. Assuming that the initial data $u_0$ belongs to the critical space $L^{3}$ almost surely, we construct a unique local-in-time…

Given an initial data $v_0$ with vorticity $\Om_0=\na\times v_0$ in $L^{\frac 3 2},$ (which implies that $v_0$ belongs to the Sobolev space $H^{\frac12}$), we prove that the solution $v$ given by the classical Fujita-Kato theorem blows up…

Assuming that ${T}$ is a potential blow up time for the Navier-Stokes system in half-space, we show that $L_{3}$-norm of the velocity field goes to $\infty$ as time t approaches $T$.

In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear…

We give sufficient conditions on the initial data for the decay in time of the kinetic energy, $E$, of solutions to the system of equations describing the motion of a rigid body in a Navier-Stokes liquid. More precisely, assuming the…

In this paper, we study existence times of strong solutions of the three-dimensional Navier-Stokes equations in time-varying analytic Gevrey classes based on Sobolev spaces $H^s, s> \frac{1}{2}$. This complements the seminal work of Foias…

In this work we investigate the question of preventing the three-dimensional, incompressible Navier-Stokes equations from developing singularities, by controlling one component of the velocity field only, in space-time scale invariant…

We establish various results concerning the uniqueness of zero velocity solutions for the static barotropic Navier--Stokes system. Some of them can be seen as Liouville-type theorems for problems in unbounded physical space.

We establish the first finite-time blow-up results for generalized 3D stochastic fractional Navier-Stokes equations \[ \Caputo \mathbf{u} = -(\mathbf{u} \cdot \nabla)\mathbf{u} - \nabla p + \nu \fLaplacian \mathbf{u} +…

It is known that smooth solutions to the non-isentropic Navier-Stokes equations without heat-conductivity may lose their regularities in finite time in the presence of vacuum. However, in spite of the recent progress on such blowup…

The main subject of this paper concerns the establishment of certain classes of initial data, which grant short time uniqueness of the associated weak Leray-Hopf solutions of the three dimensional Navier-Stokes equations. In particular, our…

In this paper, we consider the initial-boundary value problem to the nonhomogeneous incompressible Navier-Stokes equations. Local strong solutions are established, for any initial data $(\rho_0, u_0)\in (W^{1,\gamma} \cap L^\infty)\times…