Related papers: Partial regularity for Navier-Stokes and liquid cr…
This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet…
In 2001, H. Koch and D. Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in ${\mathbb{R}}^d$ for initial data small enough in $BMO^{-1}$. We show in this article that the Koch and Tataru…
We consider the 3D incompressible hypodissipative Navier-Stokes equations, when the dissipation is given as a fractional Laplacian $(-\Delta )^s$ for $s\in (\frac34,1)$, and we provide a new bootstrapping scheme that makes it possible to…
Consider an axis-symmetric suitable weak solution of 3D incompressible Navier-Stokes equation with nontrivial swirl. If the solution satisfies a slightly supercritical assumption, we will prove that v is regular. This extends the results of…
A new type of low-regularity integrator is proposed for Navier-Stokes equations, coupled with a stabilized finite element method in space. Unlike the other low-regularity integrators for nonlinear dispersive equations, which are all fully…
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…
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…
We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly…
This paper develops a new approach to show the maximal regularity theorem of the Stokes equations with free boundary conditions in the half-space $\mathbb R^d_+$, $d \ge 2$, within the $L_1$-in-time and $\mathcal B^s_{q, 1}$-in-space…
In this paper, we consider the local regularity of suitable weak solutions to the 3D incompressible Navier-Stokes equations. By means of the local pressure projection introduced by Wolf in [15,16], we present a $\varepsilon$-regularity…
This paper establishes a complete framework for infinitely nested logarithmic improvements to regularity criteria for the three-dimensional incompressible Navier-Stokes equations. Building upon our previous works on logarithmically improved…
Motivated by Kolmogorov's theory of turbulence we present a unified approach to the regularity problems for the 3D Navier-Stokes and Euler equations. We introduce a dissipation wavenumber $\Lambda (t)$ that separates low modes where the…
Forward self-similar and discretely self-similar weak solutions of the Navier-Stokes equations are known to exist globally in time for large self-similar and discretely self-similar initial data and are known to be regular outside of a…
In this paper, we consider the linearized compressible Navier-Stokes equations with non-slip boundary conditions in the half space $ \mathbb{R}^N_{+}$. We prove the generation of a continous analytic semigroup associated with this…
Starting from the partial regularity results for suitable weak solutions to the Navier-Stokes Cauchy problem by Caffarelli, Kohn and Nirenberg, as a corollary, under suitable assumptions of local character on the initial data, we prove a…
We prove an $\epsilon$-regularity criterion for the 3D Navier-Stokes equations in terms of initial data. It shows that if a scaled local $L^2$ norm of initial data is sufficiently small around the origin, a suitable weak solution is regular…
We study an initial-boundary value problem for the incompressible Navier-Stokes-Cahn-Hilliard system with non-constant density proposed by Abels, Garcke and Gr\"{u}n in 2012. This model arises in the diffuse interface theory for binary…
In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous…
In this paper, we study the Landau equation under the Navier-Stokes scaling in the torus for hard and moderately soft potentials. More precisely, we investigate the Cauchy theory in a perturbative framework and establish some new short time…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…