The Spectrum of a linearized 2D Euler operator
Y. Latushkin, Y. Li, M. Stanislavova
Abstract
We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier modes. We prove that the essential spectrum coincides with the imaginary axis, and give an estimate from above for the number of isolated nonimaginary eigenvalues. In addition, we prove that the spectral mapping theorem holds for the group generated by the linearized 2D Euler operator.
Create a lesson
Related papers
Positive normalized solutions for a singular regularized p(x)-Laplacian Dirichlet problem
Mustafa Avci
Regularity for axisymmetric Navier-Stokes with an Euler length
Peter Constantin, Mihaela Ignatova, Vlad Vicol
Existence of strong initial traces for stochastic conservation laws
Marko Erceg, Nikola Konatar, Kenneth Karlsen et al.
Asymptotics of nonlocal nonlinear Robin energies
Serena Dipierro, Giuseppe Spadaro, Enrico Valdinoci
Discontinuity of the Vlasov--Poisson Flow in LxpLv∞
Ke Chen, In-Jee Jeong, Quoc-Hung Nguyen et al.
Dense orbits for scale-invariant rotationally symmetric solutions of the 2D Euler equations
Ibrahim Suleiman