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The pointwise estimates of solutions to the Cauchy problem of a chemotaxis model

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Abstract

This paper deals with an attraction-repulsion chemotaxis model (ARC) in multi-dimensions. By Duhamel’s principle, the implicit expression of the solution to (ARC) is given. With the method of Green’s function, the authors obtain the pointwise estimates of solutions to the Cauchy problem (ARC) for small initial data, which yield the W s,p (1 ≤ p ≤ ∞) decay properties of solutions.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Renkun Shi & Weike Wang

Authors
  1. Renkun Shi
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  2. Weike Wang
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Correspondence to Renkun Shi.

Additional information

The research of R. K. Shi was supported by the National Natural Science Foundation of China (No. 111 71213). The research of W. K. Wang was supported by the National Natural Science Foundation of China (No. 11231006) and the National Research Foundation for the Doctoral Program of Higher Education of China (No. 20130073110073).

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Shi, R., Wang, W. The pointwise estimates of solutions to the Cauchy problem of a chemotaxis model. Chin. Ann. Math. Ser. B 37, 111–124 (2016). https://doi.org/10.1007/s11401-015-0938-0

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  • DOI: https://doi.org/10.1007/s11401-015-0938-0

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