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Mathematical Fluid Dynamics, Present and Future pp 377–399Cite as

Weak Solutions to Problems Involving Inviscid Fluids

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 183))

Abstract

We consider an abstract functional-differential equation derived from the pressureless Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method of convex integration we show the existence of infinitely many weak solutions for prescribed initial data and kinetic energy.

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Acknowledgements

The research of E.F. leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC Grant Agreement 320078.

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Authors and Affiliations

  1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

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  1. Eduard Feireisl
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Correspondence to Eduard Feireisl .

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Editors and Affiliations

  1. Department of Mathematics, Waseda University, Tokyo, Japan

    Yoshihiro Shibata

  2. Department of Mathematics, Waseda University, Tokyo, Japan

    Yukihito Suzuki

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Feireisl, E. (2016). Weak Solutions to Problems Involving Inviscid Fluids. In: Shibata, Y., Suzuki, Y. (eds) Mathematical Fluid Dynamics, Present and Future. Springer Proceedings in Mathematics & Statistics, vol 183. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56457-7_13

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