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Continuous Dependence on Initial Data in Fluid–Structure Motions

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Abstract

We prove a continuous dependence theorem for weak solutions of equations governing a fluid–structure interaction problem in two spatial dimensions. The proof is based on a priori estimates which, in particular, convey uniqueness of weak solutions. The estimates are obtained using Eulerian coordinates, without remapping the problem into a fixed domain.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University and Purdue University at Indianapolis, 402 N. Blackford St., LD 270, Indianapolis, IN, 46202-3267, USA

    Giovanna Guidoboni

  2. Dipartimento di Matematica, Università di Ferrara, via Machiavelli 35, 44100, Ferrara, Italy

    Marcello Guidorzi & Mariarosaria Padula

Authors
  1. Giovanna Guidoboni
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  2. Marcello Guidorzi
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  3. Mariarosaria Padula
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Correspondence to Mariarosaria Padula.

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Guidoboni, G., Guidorzi, M. & Padula, M. Continuous Dependence on Initial Data in Fluid–Structure Motions. J. Math. Fluid Mech. 14, 1–32 (2012). https://doi.org/10.1007/s00021-010-0031-0

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