Temporal asymptotics for the p'th power newtonian fluid in one space dimension
Marta Lewicka and Stephen J. Watson
Note: abridged version
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Submission date: 30. Aug. 2001
published in: Zeitschrift für Angewandte Mathematik und Physik, 54 (2003) 4, p. 633-651
DOI number (of the published article): 10.1007/s00033-003-1149-1
MSC-Numbers: 76N10, 35Q10
Keywords and phrases: a priori bounds, navier-stokes, newtonian fluid, p'th power gas, temporal asymptotics
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In this paper we consider a variety of initial-boundary value problems for the p'th power Newtonian fluid in one space dimension. We extend previously known results for the ideal gas case to a more general p'th power gas law, subject to the pinned endpoints and Dirichlet or Neumann temperature boundary conditions. The exponential convergence of the temperature, velocity and density is established for generic initial data. The estimates for different boundary conditions are presented in a unified manner.