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We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a $C^\infty$ initial datum which admits infinitely many bounded admissible weak solutions.
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1994
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1994
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De Lellis, C., Székelyhidi, L.: The Euler equations as a differential inclusion
2009
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Dafermos, C. M.: Hyperbolic conservation laws in continuum physics
2010
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De Lellis, C., Székelyhidi, L.: On admissibility criteria for weak solutions of the Euler equations
2010
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Székelyhidi, L.: Weak solutions to the incompressible Euler equations with vortex sheet initial data
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De Lellis, C., Székelyhidi, L. Jr.: Dissipative continuous Euler flows
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Chiodaroli, E.: A counterexample to well–posedness of entropy solutions to the compressible Euler system
2014
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Chiodaroli, E., Kreml, O.: On the energy dissipation rate of solutions to the compressible isentropic Euler system
2014
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Feireisl, E.: Maximal dissipation and well-posedness for the compressible Euler system
2014
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Buckmaster, T.: Onsager’s conjecture almost everywhere in time
2015
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Buckmaster, T., De Lellis, C., Isett, P., Székelyhidi, L. Jr.: Anomalous dissipation for 1/5-holder Euler flows
2015
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Chiodaroli, E., De Lellis, C., Kreml, O.: Global ill-posedness of the isentropic system of gas dynamics
Isett, P.: A proof of Onsager’s conjecture
2016
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Chiodaroli, E., Gosse, L.,: A numerical glimpse at some non-standard solutions to compressible Euler equations
2017
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Daneri, S., Székelyhidi, L. Jr.: Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations
2017
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Feireisl, E., Gwaizda, P., Świerczewska-Gwiazda, A., Wiedemann, E.: Regularity and energy conservation for the compressible Euler equations
2017
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Isett, P.: Nonuniqueness and existence of continuous, globally dissipative Euler flows
2017
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2015
Cited alongside, same era.
Buckmaster, T., De Lellis, C., Székelyhidi, L. Jr.: Dissipative Euler flows with Onsager-critical spatial regularity
2016
Cited alongside, same era.
Buckmaster, T., De Lellis, C., Székelyhidi, L. Jr., Vicol, V.: Onsager’s conjecture for admissible weak solutions
2019
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