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- W2152513668 abstract "Many applications of time-analyticity of solutions of dissipative evolution equations raise the question of estimating the uniform time-analyticity radius of solutions. For instance, the rate of decay of power spectrum, which is the quantity often measured in experiments, can be estimated in terms of the uniform time-analyticity radius [1]. Also, in [8,10,11], uniform time-analyticity plays a role in establishing algebraic approximations of attractors. Moreover, a rigorous explicit estimate of the time-analyticity domain is important for constructing these approximations since better analyticity estimates lead to better estimates on accuracy. In this note, we address time-analyticity of solutions of the Kuramoto–Sivashinsky equation ut+uxxxx+uxx+uux=0 with the initial data u0 ∈Lp(R). Since the time-analyticity is not a local property, it is expected that the analyticity domain will depend on the initial data. In Theorem 2.1, we provide this estimate as a function of the initial data and p. In the case p = 2, this has been obtained in [6,9,15] by energy estimates on rays in the complex plane. Here we estimate the fundamental solutions corresponding to each ray. In order to optimize the shape of domains, we employ the fact that the fundamental solution of the main linear part is contracting along every ray if p = 2, and then use the Riesz interpolation theorem to cover other values of p (cf. Lemma 3.3)." @default.
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- W2152513668 date "2003-01-01" @default.
- W2152513668 modified "2023-09-28" @default.
- W2152513668 title "A remark on time-analyticity for the Kuramoto–Sivashinsky equation" @default.
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- W2152513668 doi "https://doi.org/10.1016/s0362-546x(01)00910-5" @default.
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