2023/07/10 by Shyam Sundar Ghoshal, Ghoshal, Shyam Sundar, Stéphane Junca +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2307.04834
openalex publication_date 2023/07/10 · openalex created_date 2023/07/13 · openalex updated_date 2026/07/28
For the Burgers equation, the entropy solution becomes instantly BV with only L^∞ initial data. For conservation laws with genuinely nonlinear discontinuous flux, it is well known that the BV regularity of entropy solutions is lost. Recently, this regularity has been proved to be fractional with s = 1/2. Moreover, for less nonlinear flux the solution has still a fractional regularity 0 < s ≤ 1/2. The resulting general rule is the regularity of entropy solutions for a discontinuous flux is less than for a smooth flux. In this paper, an optimal geometric condition on the discontinuous flux is used to recover the same regularity as for the smooth flux with the same kind of nonlinearity.