Abstract
In this chapter we prove that the uniform Evans condition of Definition 6.3.5 implies uniform estimates for the solutions of (6.1.2). Moreover, these estimates are optimal from the point of view of parabolic smoothness. The proof relies on the use of symmetrizers, which are constructed as Fourier multipliers. A corollary of the construction of symmetrizers is the continuous extendability of the spectral spaces E_ stated in Lemma 6.2.8 and Theorem 6.4.8 (see [MZ2]). In this chapter, we always suppose that Assumption 5.1.1 is satisfied and we consider the linearized equations (6.1.2) around a profile w that satisfies (6.1.1).
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© 2004 Springer Science+Business Media New York
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Métivier, G. (2004). Stability Estimates. In: Small Viscosity and Boundary Layer Methods. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8214-9_7
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DOI: https://doi.org/10.1007/978-0-8176-8214-9_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6496-5
Online ISBN: 978-0-8176-8214-9
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