Abstract
We consider the problem of motion of several rigid bodies immersed in a perfect compressible fluid. Using the method of convex integration we establish the existence of infinitely many weak solutions with a priori prescribed motion of rigid bodies. In particular, the dynamics is completely time–reversible at the motion of rigid bodies although the solutions comply with the standard entropy admissibility criterion.
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References
Chemetov, N.V., and Nečasová, Š: The motion of the rigid body in the viscous fluid including collisions. Global solvability result. Nonlinear Anal. Real World Appl. 34, 416–445 (2017)
Chiodaroli, E.: A counterexample to well-posedness of entropy solutions to the compressible Euler system. J. Hyperbolic Differ. Equ. 11(3), 493–519 (2014)
De Lellis, C., Székelyhidi, L., Jr.: On admissibility criteria for weak solutions of the Euler equations. Arch. Ration. Mech. Anal. 195(1), 225–260 (2010)
Evans, L.C., Gariepy, R.F.: Measure theory and fine properties of functions. CRC Press, Boca Raton (1992)
Feireisl, E.: Weak solutions to problems involving inviscid fluids. In: Mathematical Fluid Dynamics. Present and Future, volume 183 of Springer Proceedings in Mathematics and Statistics, pp. 377–399. Springer, New York (2016)
Galdi, G.P.: On the motion of a rigid body in a viscous liquid: a mathematical analysis with applications. In: Handbook of mathematical fluid dynamics, Vol. 1, 653–791, North-Holland, Amsterdam, (2002)
Hillairet, M.: Topics in the mathematical theory of interactions of incompressible viscous fluid with rigid bodies. In: Fluid-structure interaction and biomedical applications, Adv. Math. Fluid Mech., 257–320, Birkhäuser/Springer, Basel, (2014)
Houot, J.G., San Martin, J., Tucsnak, M.: Existence of solutions for the equations modeling the motion of rigid bodies in an ideal fluid. J. Funct. Anal. 259, 2856–2885 (2010)
Ortega, J., Rosier, L., and Takahashi, T.: On the motion of a ridgid body in a bidimensional incompressible perfect fluid. Ann. l. H. Poincaré AN24, 139–165 (2007)
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The research of E.F. and V.M. leading to these results has received funding from the Czech Sciences Foundation (GAČR), Grant Agreement 18–05974S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.
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Feireisl, E., Mácha, V. On the motion of rigid bodies in a perfect fluid. Nonlinear Differ. Equ. Appl. 28, 35 (2021). https://doi.org/10.1007/s00030-021-00697-5
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DOI: https://doi.org/10.1007/s00030-021-00697-5