On the growth rate of solutions for 2D incompressible Euler equations
نویسنده
چکیده
We consider the Cauchy problem of 2 dimensional incompressible Euler equations. We study the problem of growth rate of high Sobolev norms of the solutions. A well-known result that is implicit in [J. T. Beals ,T. Kato and A. Majda, Comm. Math. Phys. 94 (1984), 61-66] is the double exponential rate. An open question that has been asked by Tao is wether we can get an exponential rate. In this paper, we show that the high Sobolev norms at most grow at an almost exponential rate exp (Ct1+δ) for any δ > 0. Keyword: incompressible Euler equations, growth rate, exponential rate. AMS subject classifications :35Q35
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 کاملAn incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time ...
متن کاملThe Inviscid Limit for Two-dimensional Incompressible Fluids with Unbounded Vorticity
In [C2], Chemin shows that solutions of the Navier-Stokes equations in R for an incompressible fluid whose initial vorticity lies in L ∩ L∞ converge in the zero-viscosity limit in the L–norm to a solution of the Euler equations, convergence being uniform over any finite time interval. In [Y2], Yudovich assumes an initial vorticity lying in L for all p ≥ p0, and establishes the uniqueness of sol...
متن کاملPressure-Velocity Coupled Finite Volume Solution of Steady Incompressible Invscid Flow Using Artificial Compressibility Technique
Application of the computer simulation for solving the incompressible flow problems motivates developing efficient and accurate numerical models. The set of Inviscid Incompressible Euler equations can be applied for wide range of engineering applications. For the steady state problems, the equation of continuity can be simultaneously solved with the equations of motion in a coupled manner using...
متن کاملOn 2d incompressible Euler equations with partial damping
We consider various questions about the 2d incompressible Navier-Stokes and Euler equations on a torus when dissipation is removed from or added to some of the Fourier modes.
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 2008