2011/03/21 by Jolanta Socala, Jolanta Socała, Wojciech M. Zajączkowski +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35D05 #35D10 #35K05 #35K20 #35Q30 #76D03 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Boundary value problem #Bounded function #Convection #Cylinder #Domain (mathematical analysis) #FOS: Mathematics #FOS: Physical sciences #Geometry #Heat equation #Homogeneous #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Mechanics #Navier–Stokes equations #Neumann boundary condition #Numerical methods in inverse problems #Physics #Slip (aerodynamics) #Stability and Controllability of Differential Equations #Thermodynamics #math-ph #math.AP #math.MP #msc:35D05 #msc:35D10 #msc:35K05 #msc:35K20 #msc:35Q30 #msc:76D03 #msc:76D05
paper · pdf · doi:10.48550/arxiv.1103.4022
arxiv created 2011/03/21 · openalex publication_date 2011/03/21 · arxiv updated 2011/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine the Navier-Stokes equations with homogeneous slip boundary\nconditions coupled with the heat equation with homogeneous Neumann conditions\nin a bounded domain in R3. The considered domain is a cylinder with\nx3-axis. The aim of this paper is to show long time estimates without\nsmallness of the initial velocity, the initial temperature and the external\nforce. To prove the estimate we need however smallness of L2 norms of\nderivatives with respect to x3 of the initial velocity, the initial\ntemperature and the external force.\n