2009/09/10 by Rinaldo M. Colombo, Colombo, Rinaldo M., Francesca Marcellini +1
Computer Science · Mathematics · #35L65 #76N10 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.0909.1980
openalex publication_date 2009/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the p-system describing the subsonic flow of a fluid in a pipe with section a = a(x). We prove that the resulting Cauchy problem generates a Lipschitz semigroup, provided the total variation of the initial datum and the oscillation of a are small. An explicit estimate on the bound of the total variation of a is provided, showing that at lower fluid speeds, higher total variations of a are acceptable. An example shows that the bound on TV(a) is mandatory, for otherwise the total variation of the solution may grow arbitrarily.