Infinite-energy 2d Statistical Solutions to the Equations of Incompressible Fluids
نویسنده
چکیده
Abstract. We develop the concept of an infinite-energy statistical solution to the Navier-Stokes and Euler equations in the whole plane. We use a velocity formulation with enough generality to encompass initial velocities having bounded vorticity, which includes the important special case of vortex patch initial data. Our approach is to use well-studied properties of statistical solutions in a ball of radius R to construct, in the limit as R goes to infinity, an infinite-energy solution to the Navier-Stokes equations. We then construct an infinite-energy statistical solution to the Euler equations by making a vanishing viscosity argument.
منابع مشابه
Comparison of three different numerical schemes for 2D steady incompressible lid-driven cavity flow
In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...
متن کاملTraveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids
We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of ...
متن کاملHölder Continuity of Solutions of 2D Navier-Stokes Equations with Singular Forcing
We discuss the regularity of solutions of 2D incompressible NavierStokes equations forced by singular forces. The problem is motivated by the study of complex fluids modeled by the Navier-Stokes equations coupled to a nonlinear Fokker-Planck equation describing microscopic corpora embedded in the fluid. This leads naturally to bounded added stress and hence to W forcing of the Navier-Stokes equ...
متن کاملOn Strong Solutions of the Differential Equations Modeling the Steady Flow of Certain Incompressible Generalized Newtonian Fluids
A system of nonautonomous partial differential equations describing the steady flow of an incompressible fluid is considered. The existence of a strong solution of that system is proved under suitable assumptions on the data. In the 2D-case this solution turns out to be of class C1,α. §
متن کاملGlobal Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation
Abstract. This paper studies the global existence and regularity of classical solutions to the 2D incompressible magneto-micropolar equations with partial dissipation. The magneto-micropolar equations model the motion of electrically conducting micropolar fluids in the presence of a magnetic field. When there is only partial dissipation, the global regularity problem can be quite difficult. We ...
متن کامل