Fonctions de Lyapunov pour les équations de Navier-Stokes
Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases
We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in terms of the...
Fourier-Chebyshev pseudospectral methods for the two-dimensional Navier-Stokes equations
Global attractor for Navier-Stokes equations in cylindrical domains
Global and regular solutions of the Navier-Stokes system in cylindrical domains have already been obtained under the assumption of smallness of (1) the derivative of the velocity field with respect to the variable along the axis of cylinder, (2) the derivative of force field with respect to the variable along the axis of the cylinder and (3) the projection of the force field on the axis of the cylinder restricted to the part of the boundary perpendicular to the axis of the cylinder. With the same...
Global attractor for the Navier-Stokes equations in a cylindrical pipe
Global existence of regular special solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has already been shown. In this paper we prove the existence of the global attractor for the Navier-Stokes equations and convergence of the solution to a stationary solution.
Global existence for a nuclear fluid in one dimension: the case
We consider a simplified one-dimensional thermal model of nuclear matter, described by a system of Navier-Stokes-Poisson type, with a non monotone equation of state due to an effective nuclear interaction. We prove the existence of globally defined (large) solutions of the corresponding free boundary problem, with an exterior pressure which is not required to be positive, provided sufficient thermal dissipation is present. We give also a partial description of the asymptotic behaviour of the system,...
Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder
Global existence of regular solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe with large inflow and outflow is shown. To prove the long time existence we need smallness of derivatives, with respect to the variable along the axis of the cylinder, of the external force and of the initial velocity in L₂-norms. Moreover, we need smallness of derivatives of inflow and outflow with respect to tangent directions to the boundary and with...
Global existence of axially symmetric solutions to Navier-Stokes equations with large angular component of velocity
Global existence of axially symmetric solutions to the Navier-Stokes equations in a cylinder with the axis of symmetry removed is proved. The solutions satisfy the ideal slip conditions on the boundary. We underline that there is no restriction on the angular component of velocity. We obtain two kinds of existence results. First, under assumptions necessary for the existence of weak solutions, we prove that the velocity belongs to , so it satisfies the Serrin condition. Next, increasing regularity...
Global existence of solutions to Navier-Stokes equations in cylindrical domains
We prove the existence of global and regular solutions to the Navier-Stokes equations in cylindrical type domains under boundary slip conditions, where coordinates are chosen so that the x₃-axis is parallel to the axis of the cylinder. Regular solutions have already been obtained on the interval [0,T], where T > 0 is large, on the assumption that the L₂-norms of the third component of the force field, of derivatives of the force field, and of the velocity field with respect to the direction of...
Global free boundary problem for incompressible magnetohydrodynamics [Book]
Global regular nonstationary flow for the Navier-Stokes equations in a cylindrical pipe
Global existence of regular solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe with large inflow and outflow is shown. Global existence is proved in two steps. First, by the Leray-Schauder fixed point theorem we prove local existence with large existence time. Next, the local solution is prolonged step by step. The existence is proved without any restrictions on the magnitudes of the inflow, outflow, external force and initial...
Global regular solutions to the Navier-Stokes equations in a cylinder
The existence and uniqueness of solutions to the Navier-Stokes equations in a cylinder Ω and with boundary slip conditions is proved. Assuming that the azimuthal derivative of cylindrical coordinates and azimuthal coordinate of the initial velocity and the external force are sufficiently small we prove long time existence of regular solutions such that the velocity belongs to and the gradient of the pressure to . We prove the existence of solutions without any restrictions on the lengths of the...
Global regularity for the 3D inhomogeneous incompressible Navier-Stokes equations with damping
This paper is concerned with the 3D inhomogeneous incompressible Navier-Stokes equations with damping. We find a range of parameters to guarantee the existence of global strong solutions of the Cauchy problem for large initial velocity and external force as well as prove the uniqueness of the strong solutions. This is an extension of the theorem for the existence and uniqueness of the 3D incompressible Navier-Stokes equations with damping to inhomogeneous viscous incompressible fluids.
Global regularity of the Navier-Stokes equation on thin three-dimensional domains with periodic boundary conditions.
Global solutions, structure of initial data and the Navier-Stokes equations
In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations.
Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions [Book]
Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries.
Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence
Global well-posedness for the 2-D Boussinesq system with temperature-dependent thermal diffusivity
We prove the global well-posedness of the 2-D Boussinesq system with temperature dependent thermal diffusivity and zero viscosity coefficient.
Globalization of SQP-methods in control of the instationary Navier-Stokes equations
A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the a priori formidable SQP-step can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical test demonstrates the feasibility...