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Stochastic partial differential equations with gradient driven by space-time fractional noises

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Abstract

We establish a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises, where we suppose that the drift term contains a gradient and satisfies certain non-Lipschitz condition. We prove the strong existence and uniqueness and joint Hölder continuity of the solution to the SPDEs.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11571190, 11771218, 11771018, 12061004), the Natural Science Foundation of Ningxia (No. 2020AAC03230), and the Major Research Project for North Minzu University (No. ZDZX201902).

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Yiming Jiang

  2. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China

    Xu Yang

Authors
  1. Yiming Jiang
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  2. Xu Yang
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Correspondence to Xu Yang.

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Jiang, Y., Yang, X. Stochastic partial differential equations with gradient driven by space-time fractional noises. Front. Math. China 16, 479–497 (2021). https://doi.org/10.1007/s11464-021-0875-z

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  • DOI: https://doi.org/10.1007/s11464-021-0875-z

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