2021/03/18 by Corrado Lattanzio, Lattanzio, Corrado, Delyan Zhelyazov +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2103.10386
openalex publication_date 2021/03/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper we investigate spectral stability of traveling wave solutions\nto 1-D quantum hydrodynamics system with nonlinear viscosity in the\n(\ρ,u), that is, density and velocity, variables. We derive a sufficient\ncondition for the stability of the essential spectrum and we estimate the\nmaximum modulus of eigenvalues with non-negative real part. In addition, we\npresent numerical computations of the Evans function in sufficiently large\ndomain of the unstable half-plane and show numerically that its winding number\nis (approximately) zero, thus giving a numerical evidence of point spectrum\nstability.\n