Lesfari, Ahmed The problem of the motion of a solid in an ideal fluid. Integration of the Clebsch’s case. (English) Zbl 0982.35085 NoDEA, Nonlinear Differ. Equ. Appl. 8, No. 1, 1-13 (2001). This paper deals with a geometric approach to the integration of Clebsch’s case of equations describing the motion of a solid body in an ideal fluid. This problem is defined by a nonlinear system of 6 differential equations admitting 4 polynomial first integrals. The author shows that the intersection of surface levels of these integrals can be completed to an Abelian surface, i.e., a 2-dimensional algebraic torus. Moreover, he proves that the problem can be linearized, i.e., it can be written in terms of Abelian integrals on a Prym variety of a genus 3 curve obtained naturally. Reviewer: Jorge Ferreira (Maringá) Cited in 2 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 14H40 Jacobians, Prym varieties 70E40 Integrable cases of motion in rigid body dynamics 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 70G55 Algebraic geometry methods for problems in mechanics Keywords:ideal fluid; solid motion; Prym varieties PDFBibTeX XMLCite \textit{A. Lesfari}, NoDEA, Nonlinear Differ. Equ. Appl. 8, No. 1, 1--13 (2001; Zbl 0982.35085) Full Text: DOI