相关论文: Global regularity for a logarithmically supercriti…
We consider the dissipative generalized Surface Quasi-Geostrophic equation with dissipation given by any fractional power of the Laplacian. In the inviscid limit, it is proved that anomalous dissipation of the Hamiltonian is prevented by…
The present paper is dedicated to the global large solutions and incompressible limit for the compressible Navier-Stokes system in $\mathbb{R}^d$ with $d\ge 2$. We aim at extending the work by Danchin and Mucha (Adv. Math., 320, 904--925,…
In this note we give a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data.
In this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence…
First order semi-linear coupling of scalar hypoelliptic equations of second order leads to a natural class of incompressible Navier Stokes equation systems, which encompasses systems with variable viscosity and essentially Navier Stokes…
We show existence of global strong solutions with large initial data on the irrotational part for the shallow-water system in dimension $N\geq 2$. We introduce a new notion of \textit{quasi-solutions} when the initial velocity is assumed to…
Considering the three-dimensional incompressible Navier-Stokes equations on the whole space, we address the question: is it possible to infer global regularity of a mild solution from a single approximate solution? Assuming a relatively…
This paper proves that the 3-D Navier-Stokes system has a unique global solution under an assumpution on the initial data. That allow the data to be arbitrarily large in the scale invariant space \dot{B}_{\infty,\infty}^{-1}, which contains…
We establish the existence and uniqueness of the maximal pathwise solution for an abstract nonlinear stochastic evolutional equation, which takes the two and three dimensional stochastic Navier-Stokes equations as a typical model, forced by…
This paper is devoted to the global solvability of the Navier-Stokes system with fractional Laplacian $(-\Delta)^{\alpha}$ in $\mathbb{R}^{n}$ for $n\geq2$, where the convective term has the form $(|u|^{m-1}u)\cdot\nabla u$ for $m\geq1$. By…
In this paper we consider the initial value problem of the incompressible generalized Navier-Stokes equations in torus $\mathbb{T}^d$ with $d \geq 2$. The generalized Navier-Stokes equations is obtained by replacing the standard Laplacian…
In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…
This paper is a continuation of our previous work (arXiv:2507.03505), where the global existence and incompressible limit of weak solutions to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and…
The existence of global smooth solutions to the Navier-Stokes equations (NSEs) with hyperviscosity $(-\Delta)^{\gamma}$ is open unless $\gamma $ is close to the J.-L. Lions exponent $ \frac{5}{4}$ at which the energy balance is strong…
The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…
The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…
We prove global existence of solutions to the Cauchy problem for the compressible Navier-Stokes equations in Euclidean spaces, given initial data with small norms in Besov and critical weighted Besov spaces. Global existence and a priori…
In this paper, the $2$-D isentropic Navier-Stokes systems for compressible fluids with density-dependent viscosity coefficients are considered. In particular, we assume that the viscosity coefficients are proportional to density. These…
We consider the chemotaxis-Navier-Stokes system with generalized fluid dissipation in $\mathbb{R}^3$: \begin{eqnarray*} \begin{cases} \partial_t n+u\cdot \nabla n=\Delta n- \nabla \cdot (\chi(c)n \nabla c),\\ \partial_t c+u \cdot \nabla…
We investigate the barotropic compressible Navier-Stokes equations with the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial density that is allowed to vanish, we establish the global…