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Local existence of solutions to 2D Prandtl equations in a weighted Sobolev space

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Abstract

In this work, we investigate two-dimensional nonlinear Prandtl equations on the half plane and prove the local existence of solutions by energy methods in an exponential weighted Sobolev space. We use the skill of cancellation mechanism and construct a new unknown function to overcome some difficulties respectively.

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Acknowledgements

The authors are grateful to the anonymous referees for helpful comments and suggestions that greatly improved the presentation of a previous version of the manuscript. This paper was in part supported by the National Natural Science Foundation of China with Contract Numbers 12171082 and 11971100 and the fundamental research funds for the central universities with Contract Number 2232021G-13.

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Authors and Affiliations

  1. Department of Mathematics, Donghua University, Shanghai, 201620, People’s Republic of China

    Yuming Qin

  2. Institute for Nonlinear Science, Shanghai, 201620, People’s Republic of China

    Yuming Qin

  3. College of Information Science and Technology, Donghua University, Shanghai, 201620, People’s Republic of China

    Xiaolei Dong

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  1. Yuming Qin
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Correspondence to Yuming Qin.

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Qin, Y., Dong, X. Local existence of solutions to 2D Prandtl equations in a weighted Sobolev space. Anal.Math.Phys. 12, 16 (2022). https://doi.org/10.1007/s13324-021-00615-z

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