Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Large time decay and growth for solutions of a viscous Boussinesq system
HTML articles powered by AMS MathViewer

by Lorenzo Brandolese and Maria E. Schonbek PDF
Trans. Amer. Math. Soc. 364 (2012), 5057-5090 Request permission

Abstract:

In this paper we analyze the decay and the growth for large time of weak and strong solutions to the three-dimensional viscous Boussinesq system. We show that generic solutions blow up as $t\to \infty$ in the sense that the energy and the $L^p$-norms of the velocity field grow to infinity for large time for $1\le p<3$. In the case of strong solutions we provide sharp estimates, both from above and from below, and explicit asymptotic profiles. We also show that solutions arising from $(u_0,\theta _0)$ with zero-mean for the initial temperature $\theta _0$ have a special behavior as $|x|$ or $t$ tends to infinity: contrary to the generic case, their energy dissipates to zero for large time.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 76D05, 35Q35, 35B40
  • Retrieve articles in all journals with MSC (2010): 76D05, 35Q35, 35B40
Additional Information
  • Lorenzo Brandolese
  • Affiliation: Université de Lyon, CNRS UMR 5208 Institut Camille Jordan, Université Lyon 1, 43 bd. du 11 novembre, Villeurbanne Cedex F-69622, France
  • Email: brandolese{@}math.univ-lyon1.fr
  • Maria E. Schonbek
  • Affiliation: Department of Mathematics, University of California Santa Cruz, Santa Cruz, California 95064
  • MR Author ID: 156790
  • ORCID: 0000-0002-9917-8495
  • Email: schonbek@math.ucsc.edu
  • Received by editor(s): March 18, 2010
  • Received by editor(s) in revised form: July 27, 2010
  • Published electronically: May 30, 2012
  • Additional Notes: The work of both authors was partially supported by FBF Grant SC-08-34
    The work of the second author was partially supported by NSF Grants DMS-0900909 and grant FRG-09523-503114.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 5057-5090
  • MSC (2010): Primary 76D05; Secondary 35Q35, 35B40
  • DOI: https://doi.org/10.1090/S0002-9947-2012-05432-8
  • MathSciNet review: 2931322