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Well-posedness for the 2D dissipative quasigeostrophic equations in the Besov space

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Abstract

In this paper, we consider the initial value problem of the 2D dissipative quasigeostrophic equations. Existence and uniqueness of the solution global in time are proved in the homogenous Besov space \(\dot B_{p,\infty }^{Sp} \)with small data when \(\frac{1}{2} < \alpha \leqslant 1,\frac{2}{{2\alpha - 1}} < p < \infty ,s_p = \frac{2}{p} - (2\alpha - 1)\). Our proof is based on a new characterization of the homogenous Besov space and Kato’s method.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Zhang Zhifei

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  1. Zhang Zhifei
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Correspondence to Zhang Zhifei.

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Zhifei, Z. Well-posedness for the 2D dissipative quasigeostrophic equations in the Besov space. Sci. China Ser. A-Math. 48, 1646–1655 (2005). https://doi.org/10.1360/04ys0210

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  • DOI: https://doi.org/10.1360/04ys0210

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