Uniformly Rotating Smooth Solutions for the Incompressible 2D Euler Equations
نویسندگان
چکیده
منابع مشابه
On the growth rate of solutions for 2D incompressible Euler equations
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 pap...
متن کاملRenormalized Solutions of the 2d Euler Equations
In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.
متن کاملIntegrable Structures for 2D Euler Equations of Incompressible Inviscid Fluids
The governing equation of turbulence, that we are interested in, is the incompressible 2D Navier– Stokes equation under periodic boundary conditions. We are particularly interested in investigating the dynamics of 2D Navier–Stokes equation in the infinite Reynolds number limit and of 2D Euler equation. Our approach is different from many other studies on 2D Navier–Stokes equation in which one s...
متن کاملLong-Time Existence of Smooth Solutions for the Rapidly Rotating Shallow-Water and Euler Equations
We study the stabilizing effect of rotational forcing in the nonlinear setting of twodimensional shallow-water and more general models of compressible Euler equations. In [Phys. D, 188 (2004), pp. 262–276] Liu and Tadmor have shown that the pressureless version of these equations admit a global smooth solution for a large set of subcritical initial configurations. In the present work we prove t...
متن کاملBlowup vs Illposedness of Smooth Solutions of the Incompressible Euler/Navier-Stokes Equations
We present evidence that the problem of breakdown/blowup of smooth solutions of the Euler and Navier-Stokes equations, is closely related to Hadamard’s concepts of wellposedness and illposedness. We present a combined criterion for blowup, based on detecting increasing L2-residuals and stability factors, which can be tested computationally on meshes of finite mesh size. 1 The Clay Navier-Stokes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archive for Rational Mechanics and Analysis
سال: 2018
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s00205-018-1288-3