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On the stability of equilibria to weakly coupled parabolic systems in unbounded domains

✍ Scribed by Joachim Escher; Zhaoyang Yin

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
264 KB
Volume
60
Category
Article
ISSN
0362-546X

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✦ Synopsis

We investigate weakly coupled semilinear parabolic systems in unbounded domains of R 2 or R 3 with general nonlinearities. We present several sufficient conditions on the nonlinearities which ensure the stability of the zero solution with respect to H 2 -perturbations. In addition, various examples are discussed to illustrate the scope of application of our results.

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## Abstract We consider the problem of the asymptotic behaviour in the __L__^2^‐norm of solutions of the Navier–Stokes equations. We consider perturbations to the rest state and to stationary motions. In both cases we study the initial‐boundary value problem in unbounded domains with non‐compact bo