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Physical Insight, Mathematical Modeling and Asymptotics

In: A Celebration of Mathematical Modeling

Author

Listed:
  • Ting Lu

    (New York University, Courant Institute of Mathematical Sciences)

Abstract

We review several problems in fluid mechanics to demonstrate how physical insight of a problem leads to a simplified mathematical model, which specifies the choice of the proper scalings, the small parameters and the expansion scheme. The mathematical model in turn gives a more precise description of the insight. It defines the conditions under which the model is not applicable and the necessary refinement of the model. The model allows for a systematic derivation of the leading and higher order system of equations, identifies the initial and or/boundary conditions needed for the simplified system and derives the missing condition(s) of the leading order system of equations, if any, from the compatibility condition(s) on the next order. Special emphasis is placed on the importance of formulating the correct mathematical model relevant to the physical insight and the understanding of the physical implications.

Suggested Citation

  • Ting Lu, 2004. "Physical Insight, Mathematical Modeling and Asymptotics," Springer Books, in: Dan Givoli & Marcus J. Grote & George C. Papanicolaou (ed.), A Celebration of Mathematical Modeling, pages 199-220, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0427-4_11
    DOI: 10.1007/978-94-017-0427-4_11
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