2019/08/26 by Marina Ghisi, Massimo Gobbino, Ghisi, Marina +1
Engineering · Mathematics · #26A24 #35L15 #35Q35 #76F25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #math.FA #msc:26A24 #msc:35L15 #msc:35Q35 #msc:76F25
paper · pdf · doi:10.48550/arxiv.1908.09496
37 pages -- We updated the introduction and added some extra references
openalex publication_date 2019/08/26 · arxiv created 2020/06/29 · arxiv updated 2020/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several counterexamples in analysis show the existence of some special object with some sort of pathological behavior. We present three different examples where the pathological behavior is not an isolated exception, but it is the "typical" behavior of the "generic" object in a suitable class, where here generic means residual in the sense of Baire category. The first example is the revisitation of a classical result concerning approximate differentiation. The second example is the derivative loss for solutions to linear wave equations with time-dependent Holder continuous propagation speed. The third result is the derivative loss for solutions to transport equations with non-Lipschitz velocity field.