Related papers: Global hydrostatic approximation of hyperbolic Nav…
In this paper, we study a hyperbolic version of the Navier-Stokes equations, obtained by using the approximation by relaxation of the Euler system, evolving in a thin strip domain. The formal limit of these equations is a hyperbolic Prandtl…
We consider the hyperbolic version of three-dimensional anisotropic Naver-Stokes equations in a thin strip and its hydrostatic limit that is a hyperbolic Prandtl type equations. We prove the global-in-time existence and uniqueness for the…
In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When the convex initial data with Gevrey regularity of optimal index 3/2 in x variable and Sobolev regularity in y variable, we justify the…
In this paper, we justify the limit from the Navier-Stokes system in a thin domain to the hydrostatic Navier-Stokes/Prandtl system for the convex initial data with Gevrey 9/8 regualrity in $x$.
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…
In this paper, we prove the local well-posedness of a scaled anisotropic Navier-Stokes-Maxwell system in a two-dimensional striped domain with a transverse magnetic field around $ (0,0,1)$ in Gevrey-2 class. We also justify the limit from…
We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation…
We address the local well-posedness of the hydrostatic Navier-Stokes equations. These equations, sometimes called reduced Navier-Stokes/Prandtl, appear as a formal limit of the Navier-Stokes system in thin domains, under certain constraints…
We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously…
We study an initial boundary value problem for the 3-dimensional compressible Navier-Stokes equations with hyperbolic heat conduction, where the classical Fourier law is replaced by the Cattaneo-Christov constitutive relation. We focus on…
We investigate a two-parameter hyperbolic relaxation approximation to the incompressible Navier-Stokes equations, incorporating a first-order relaxation and the artificial compressibility method. With vanishingly small perturbations of…
We consider a hyperbolic quasilinear fluid model, that arises from a delayed version for the constitutive law for the deformation tensor in the incompressible Navier-Stokes equation. We prove the existence of global strong solutions for…
We consider the non-isentropic compressible Navier-Stokes equations in two or three space dimensions for which the heat conduction of Fourier's law is replaced by Cattaneo's law and the classical Newtonian flow is replaced by a revised…
In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin striped domain. We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small…
We consider the two-phase dynamics of two incompressible and immiscible fluids. As a mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the class of diffuse-interface models. Solutions of the…
In this paper we propose a stable and robust strategy to approximate the 3d incompressible hydrostatic Euler and Navier-Stokes systems with free surface. Compared to shallow water approximation of the Navier-Stokes system, the idea is to…
The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the…
In this paper, we provide rigorous justification of the hydrostatic approximation and the derivation of primitive equations as the small aspect ratio limit of the incompressible three-dimensional Navier-Stokes equations in the anisotropic…
A hyperbolic relaxation of the classical Navier-Stokes problem in 2D bounded domain with Dirichlet boundary conditions is considered. It is proved that this relaxed problem possesses a global strong solution if the relaxation parameter is…
For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…