On some recently derived exact solutions to the Euler equations

Abstract

We present some explicit solutions with radial character in the setting of Eulerian framework to the three-dimensional nonlinear water waves in arctic regions. In particular, we focus on the motion of water waves with a moving bed and the pressure varying on free surface.

KEYWORDS:

• Arctic flow
• explicit solutions
• a moving bed

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35Q31
• 35Q35
• 76B15
• 76U05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Yanjuan Yang was supported by the National Natural Science Foundation of China (Grants No. 12201364), the Shandong Provincial Natural Science Foundation (Grant No. ZR2021QA048) and the China Postdoctoral Science Foundation (Grant No. 2021M702037).