2016/08/22 by Rolci Cipolatti, R. A. Cipolatti, Cipolatti, R. A. +12
Engineering · Mathematics · #35B40 #35Q30 #37A60 #76D06 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Applied mathematics #FOS: Mathematics #Geology #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Order (exchange) #Physics #Sobolev space #Stability and Controllability of Differential Equations #Stokes problem #Thermodynamics #Type (biology) #Uniqueness #Viscoelasticity #Weak solution #math.AP #msc:35B40 #msc:35Q30 #msc:37A60 #msc:76D06
paper · pdf · doi:10.48550/arxiv.1608.06230
Second version with very minor typographical revisions
openalex publication_date 2016/08/22 · arxiv created 2017/01/25 · arxiv updated 2017/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Stokes-type problem for a viscoelastic model of salt rocks is considered, and existence, uniqueness and regularity are investigated in the scale of L2-based Sobolev spaces. The system is transformed into a generalized Stokes problem, and the proper conditions on the parameters of the model that guarantee that the system is uniformly elliptic are given. Under those conditions, existence, uniqueness and low-order regularity are obtained under classical regularity conditions on the data, while higher-order regularity is proved under less stringent conditions than classical ones. Explicit estimates for the solution in terms of the data are given accordingly.