2021/04/25 by Huan Xu, Xu, Huan · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2104.12251
openalex publication_date 2021/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is twofold. First, we use a classical method to establish Gaussian bounds of the fundamental matrix of a generalized parabolic Lamé system with only bounded and measurable coefficients. Second, we derive a maximal L1 regularity result for the abstract Cauchy problem associated with a composite operator. In a concrete example, we also obtain maximal L1 regularity for the Lamé system, from which it follows that the Lipschitz seminorm of the solutions to the Lamé system is globally L1-in-time integrable. As an application, we use a Lagrangian approach to prove a global-in-time well-posedness result for a viscous pressureless flow provided that the initial velocity satisfies a scaling-invariant smallness condition. The method established in this paper might be a powerful tool for studying many issues arising from viscous fluids with truly variable densities.