2006/04/17 by Kevin Zumbrun, K. Zumbrun, Zumbrun, K.
Engineering · Mathematics · Physics and Astronomy · #35B35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations #math.AP #msc:35B35
paper · pdf · doi:10.48550/arxiv.math/0604375
Minor additions/corrections
openalex publication_date 2006/04/17 · arxiv created 2006/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Benzoni--Gavage, Danchin, Descombes, and Jamet have given a sufficient condition for linear and nonlinear stability of solitary wave solutions of Korteweg's model for phase-transitional isentropic gas dynamics in terms of convexity of a certain ``moment of instability'' with respect to wave speed, which is equivalent to variational stability with respect to the associated Hamiltonian energy under a partial subset of the constraints of motion; they conjecture that this condition is also necessary. Here, we compute a sharp criterion for spectral stability in terms of the second derivative of the Evans function at the origin, and show that it is equivalent to the variational condition obtained by Benzoni--Gavage et al, answering their conjecture in the positive.