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).
KeywordsImaginary Axis Pseudodifferential Operator Medium Frequency Stability Estimate Spectral Projector
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