Low Mach number limit for the compressible Navier-Stokes equation with a stationary force

Mathematics > Analysis of PDEs [Submitted on 14 Jan 2025 (v1), last revised 18 Jun 2026 (this version, v2)] Title:Low Mach number limit for the compressible Navier-Stokes equation with a stationary force View PDF HTML (experimental)Abstract:In this paper, we are concerned with the low Mach number limit for the compressible Navier-Stokes equation with a stationary force and ill-prepared initial data in the three-dimensional whole space. The convergence result of the stationary solutions toward the corresponding incompressible flow is obtained when the stationary force is small enough. Under the assumption that the initial perturbation around the stationary solution is small enough, the convergence result of the perturbation toward the corresponding perturbation around the stationary incompressible flow is obtained globally in time. The proof relies crucially on the Strichartz type estimate for the linearized semigroup around the motionless state which reflects not only its dispersive property but also dissipative properties of the linearized operator. Submission history From: Naoto Deguchi [view email][v1] Tue, 14 Jan 2025 18:50:59 UTC (24 KB) [v2] Thu, 18 Jun 2026 05:52:26 UTC (45 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.