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Abstract <p>In this paper, we discuss syzygies and quotient equations of the two-dimensional Euler system of PDEs. We use some of the previously obtained results concerning kinematic symmetries and invariants of the system to find the quotient. It follows from the theorem describing the field of differential invariants that there are ten relations (syzygies) between the second-order invariants. Choosing zero- and first-order invariants as Lie–Tresse coordinates and expressing Tresse derivatives, we obtain the quotient.</p>

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Quotient of the Two-dimensional Euler Equations

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • A. Duyunova,
  • S. Tychkov

摘要

Abstract

In this paper, we discuss syzygies and quotient equations of the two-dimensional Euler system of PDEs. We use some of the previously obtained results concerning kinematic symmetries and invariants of the system to find the quotient. It follows from the theorem describing the field of differential invariants that there are ten relations (syzygies) between the second-order invariants. Choosing zero- and first-order invariants as Lie–Tresse coordinates and expressing Tresse derivatives, we obtain the quotient.