Related papers: Well-posedness of the hydrostatic Navier-Stokes eq…
In this paper, we investigate the well-posedness theory and exponential stability for the inhomogeneous incompressible Navier-Stokes equation with only horizontal dissipative structure. Due to the lack of the vertical dissipative term and…
In this paper, we are first interested in the compressible Navier-Stokes equations with densitydependent viscosities in bounded domains with on-homogeneous Dirichlet conditions. We study the wellposedness of such models with non-constant…
We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional…
We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong…
The properties of solutions to Navier-Stokes equations, including well-posedness and Gevrey regularity, are a class of highly interesting problems. We are inspired by the location result on Triebel-Lizorkin-Lorentz space of Hobus and Saal…
We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and that the initial…
This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin 3 dimensional domain with periodic…
Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); \mathbf{W}^{-1,p}(\Omega))$ for $p$ and $q$ in appropriate parameter ranges are proven. The case of spatially…
In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the…
We are concerned with the barotropic compressible Navier-Stokes equations on the real line. Our primary goal is to establish the global well-posedness in a critical regularity framework in the case where the initial data are small…
In this paper, we are concerned with the local and global existence for the stochastic Prandtl equation in two and three dimensions, which governs the velocity field inside the boundary layer that appears in the inviscid limit of the…
The decaying speed of a single norm more truly reflects the intrinsic harmonic analysis structure of the solution of the classical incompressible Navier-Stokes equations. No previous work has been able to establish the well-posedness under…
The planar Navier-Stokes equation exhibits, in absence of external forces, a trivial asymptotics in time. Nevertheless the appearence of coherent structures suggests non-trivial intermediate asymptotics which should be explained in terms of…
In this paper, we study local well-posedness for the Navier-Stokes \linebreak equations with arbitrary initial data in homogeneous Sobolev spaces $\dot{H}^s_p(\mathbb{R}^d)$ for $d \geq 2, p > \frac{d}{2},\ {\rm and}\ \frac{d}{p} - 1 \leq s…
In this paper, we consider the almost sure well-posedness of the Cauchy problem to the Cahn-Hilliard-Navier-Stokes equation with a randomization initial data on a torus $\mathbb{T}^3$. First, we prove the local existence and uniqueness of…
This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in $\R^{N}$ with $N\geq2$. We address the question of well-posedness for {\it large} data having critical Besov regularity…
In this paper we obtain new well-possedness results concerning a linear inhomogenous Stokes-like system. These results are used to establish local well-posedness in the critical spaces for initial density $\rho_{0}$ and velocity $u_{0}$…
This paper investigates the well-posedness of the hydrostatic MHD-wave system. Unlike the standard hydrostatic MHD equations, the tangential magnetic field equation in this system is degenerate hyperbolic rather than parabolic, which leads…
In this paper, we study local well-posedness for the Navier-Stokes equations with arbitrary initial data in homogeneous Sobolev spaces $\dot{H}^s_p(\mathbb{R}^d)$ for $d \geq 2, p > \frac{d}{2},\ {\rm and}\ \frac{d}{p} - 1 \leq s <…
Relativistic Navier-Stokes equations express the conservation of the energy-momentum tensor and the particle number current in terms of the local hydrodynamic variables: temperature, fluid velocity, and the chemical potential. We show that…