Zobrazeno 1 - 10
of 52 388
pro vyhledávání: '"Euler equation"'
We study the radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler equation in the unit disc, both in the smooth setting and the patch setting. In the patch setting, we prove that every uniformly rotating patch wit
Externí odkaz:
http://arxiv.org/abs/2412.05973
In this paper, we construct a family of global solutions to the incompressible Euler equation on a standard 2-sphere. These solutions are odd-symmetric with respect to the equatorial plane and rotate with a constant angular speed around the polar axi
Externí odkaz:
http://arxiv.org/abs/2411.07645
Helical Kelvin waves were conjectured to exist for the 3D Euler equations in Lucas and Dritschel \cite{LucDri} (as well as in \cite{Chu}) by studying dispersion relation for infinitesimal linear perturbations of a circular helically symmetric vortex
Externí odkaz:
http://arxiv.org/abs/2411.02055
Autor:
Mancilla, Robinson
We derived a generalized Euler equation, $\epsilon+p=sT+\mu q+y\frac{\partial p}{\partial y}$, using the effective field theory formulation of perfect fluids. This generalization was achieved by introducing a new variable $y$ into the effective actio
Externí odkaz:
http://arxiv.org/abs/2410.06605
Autor:
Wang, Guodong
We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is the trunca
Externí odkaz:
http://arxiv.org/abs/2408.15598
Autor:
Roveri, Leonardo, Triggiano, Francesco
We consider the 2D Euler equation with bounded initial vorticity and perturbed by rough transport noise. We show that there exists a unique solution, which coincides with the starting condition advected by the Lagrangian flow. Moreover, the stability
Externí odkaz:
http://arxiv.org/abs/2410.24040
Autor:
Cao, Daomin, Wang, Guodong
In this paper, we establish three Arnold-type stability theorems for steady or rotating solutions of the incompressible Euler equation on a sphere. Specifically, we prove that if the stream function of a flow solves a semilinear elliptic equation wit
Externí odkaz:
http://arxiv.org/abs/2407.06752
Autor:
Huang, De, Tong, Jiajun
We rigorously construct the first steady traveling wave solutions of the 2D incompressible Euler equation that take the form of a contiguous vortex-patch dipole, which can be viewed as the vortex-patch counterpart of the well-known Lamb-Chaplygin dip
Externí odkaz:
http://arxiv.org/abs/2406.09849
Autor:
Konopelchenko, B. G., Ortenzi, G.
Hodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form and information on existence or absence of gradient
Externí odkaz:
http://arxiv.org/abs/2405.10646