A Stochastic Lagrangian Proof of Global Existence of the Navier-stokes Equations for Flows with Small Reynolds Number
نویسنده
چکیده
We consider the incompressible Navier-Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough we provide an elementary short proof of the existence of global in time Hölder continuous solutions. Our proof is based on the stochastic Lagrangian formulation of the Navier-Stokes equations, and works in both the two and three dimensional situation.
منابع مشابه
A Stochastic Representation for Backward Incompressible Navier-stokes Equations
By reversing the time variable we derive a stochastic representation for backward incompressible Navier-Stokes equations in terms of stochastic Lagrangian paths, which is similar to Constantin and Iyer’s forward formulations in [6]. Using this representation, a self-contained proof of local existence of solutions in Sobolev spaces are provided for incompressible Navier-Stokes equations in the w...
متن کاملSteady Flow Through Modeled Glottal Constriction
The airflow in the modeled glottal constriction was simulated by the solutions of the Navier-Stokes equations for laminar flow, and the corresponding Reynolds equations for turbulent flow in generalized, nonorthogonal coordinates using a numerical method. A two-dimensional model of laryngeal flow is considered and aerodynamic properties are calculated for both laminar and turbulent steady flows...
متن کاملAxi-symmetric Stagnation–Point Flow and Heat Transfer Obliquely Impinging on a Rotating Circular Cylinder
Laminar stagnation flow, axi-symmetrically yet obliquely impinging on a rotating circular cylinder, as well as its heat transfer is formulated as an exact solution of the Navier-Stokes equations. Rotational velocity of the cylinder is time-dependent while the surface transpiration is uniform and steady. The impinging stream is composed of a rotational axial flow superposed onto irrotational rad...
متن کاملOn the global evolution of vortex filaments, blobs, and small loops in 3D ideal flows
We consider a wide class of approximate models of evolution of singular distributions of vorticity in three dimensional incompressible fluids and we show that they have global smooth solutions. The proof exploits the existence of suitable Hamiltonian functions. The approximate models we analyze (essentially discrete and continuous vortex filaments and vortex loops) are related to some problem o...
متن کاملStochastic Models of Lagrangian Acceleration of Fluid Particle in Developed Turbulence
Modeling statistical properties of motion of a Lagrangian particle advected by a high-Reynolds-number flow is of much practical interest and complement traditional studies of turbulence made in Eulerian framework. The strong and nonlocal character of Lagrangian particle coupling due to pressure effects makes the main obstacle to derive turbulence statistics from the three-dimensional Navier-Sto...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007