Decay estimates for steady magnetohydrodynamic pipe flow

✍ Scribed by J.C. Song

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 173 KB
• Volume: 54
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(03)00124-x

✦ Synopsis

This paper establishes exponential decay bounds for steady magnetohydrodynamic pipe ow when homogeneous lateral surface boundary conditions are applied. In the spirit of earlier work of Ames and Payne (SIAM J. Math. Anal. 20 (1989) 789) and Horgan and Wheeler (SIAM J. Appl. Math. 35 (1978) 97), the decay to fully developed ow as a function of distance from the entry section is investigated. Here, it is not assumed that the ow is fully developed at the exit section. Energy inequalities are derived that lead to estimates for the "energy" associated with the velocity and magnetic ÿeld represented by the di erence between the entrance ow and the fully developed ow in a portion of the pipe near the exit section. This paper also indicates how to bound the total energy.