Harmonic solutions and weak solutions of two-dimensional rotational incompressible Euler equations

Yang CHEN; Yunhu WANG; Man Wai YUEN

doi:10.1016/j.padiff.2022.100336

Harmonic solutions and weak solutions of two-dimensional rotational incompressible Euler equations

Yang CHEN
, Yunhu WANG
, Man Wai YUEN

Department of Mathematics and Information Technology (MIT)

Research output: Contribution to journal › Articles › peer-review

Abstract

In this paper, two families of exact solutions to two-dimensional incompressible rotational Euler equations are constructed by connecting the Euler equations with the Laplace equation via a stream function. The constituent solutions in the first family are smooth, orthogonal, and conjugate harmonic solutions, while their constituent velocities are nonlinear with respect to the spatial variables. The second family are weak solutions in the distribution sense. Copyright © 2022 The Author(s).

Original language	English
Article number	100336
Journal	Partial Differential Equations in Applied Mathematics
Volume	5
Early online date	16 Mar 2022
DOIs	https://doi.org/10.1016/j.padiff.2022.100336
Publication status	Published - Jun 2022

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 4 Quality Education

Keywords

Euler equations
Laplace equation
Weak solutions

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10.1016/j.padiff.2022.100336Licence: CC BY

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published version

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abstract = "In this paper, two families of exact solutions to two-dimensional incompressible rotational Euler equations are constructed by connecting the Euler equations with the Laplace equation via a stream function. The constituent solutions in the first family are smooth, orthogonal, and conjugate harmonic solutions, while their constituent velocities are nonlinear with respect to the spatial variables. The second family are weak solutions in the distribution sense. Copyright {\textcopyright} 2022 The Author(s).",

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AB - In this paper, two families of exact solutions to two-dimensional incompressible rotational Euler equations are constructed by connecting the Euler equations with the Laplace equation via a stream function. The constituent solutions in the first family are smooth, orthogonal, and conjugate harmonic solutions, while their constituent velocities are nonlinear with respect to the spatial variables. The second family are weak solutions in the distribution sense. Copyright © 2022 The Author(s).

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U2 - 10.1016/j.padiff.2022.100336

DO - 10.1016/j.padiff.2022.100336

M3 - Articles

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JO - Partial Differential Equations in Applied Mathematics

JF - Partial Differential Equations in Applied Mathematics

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Harmonic solutions and weak solutions of two-dimensional rotational incompressible Euler equations

Abstract

UN SDGs

Keywords

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