2016/01/14 by Alessandro Morando, Morando, Alessandro, Paolo Secchi +3
Earth and Planetary Sciences · Mathematics · #35Q35 #35R35 #76B03 #76E17 #76E25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1601.03674
openalex publication_date 2016/01/14 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The paper is concerned with the free boundary problem for 2D current-vortex\nsheets in ideal incompressible magneto-hydrodynamics near the transition point\nbetween the linearized stability and instability. In order to study the\ndynamics of the discontinuity near the onset of the instability, Hunter and\nThoo have introduced an asymptotic quadratically nonlinear integro-differential\nequation for the amplitude of small perturbations of the planar discontinuity.\nThe local-in-time existence of smooth solutions to the Cauchy problem for the\namplitude equation was already shown. In the present paper we prove the\ncontinuous dependence in strong norm of solutions on the initial data. This\ncompletes the proof of the well-posedness of the problem in the classical sense\nof Hadamard.\n