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AMCS Seminar| On weak solutions to general hyperbolic systems and energy/entropy conservation

Start Date: October 17, 2017
End Date: October 17, 2017

By Professor Agnieszka Gwiazda (University of Warsaw)
 
A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second law of thermodynamics. They are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake a role of a physical admissibility condition for weak solutions. We want to discuss what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality. An archetypal example of such result was derived for the incompressible Euler system by Constantin et al. ([1]) in the context of the seminal Onsager's conjecture. [1] P. Constantin, W. E, and E. S. Titi. Onsager’s conjecture on the energy conservation for solutions of Euler’s equation. Comm. Math. Phys., 1994. [2] E. Feireisl, P. Gwiazda, A. Swierczewska-Gwiazda, and E. Wiedemann. Regularity and Energy Conservation for the Compressible Euler Equations. Arch. Ration. Mech. Anal., 223(3):1–21, 2017 [3] P. Gwiazda, M. Michálek, A. Swierczewska-Gwiazda. A note on weak solutions of conservation laws and energy/entropy conservation, arXiv:1706.10154 Speaker bio: A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second law of thermodynamics. They are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake a role of a physical admissibility condition for weak solutions. We want to discuss what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality. An archetypal example of such result was derived for the incompressible Euler system by Constantin et al. ([1]) in the context of the seminal Onsager's conjecture. [1] P. Constantin, W. E, and E. S. Titi. Onsager’s conjecture on the energy conservation for solutions of Euler’s equation. Comm. Math. Phys., 1994. [2] E. Feireisl, P. Gwiazda, A. Swierczewska-Gwiazda, and E. Wiedemann. Regularity and Energy Conservation for the Compressible Euler Equations. Arch. Ration. Mech. Anal., 223(3):1–21, 2017 [3] P. Gwiazda, M. Michálek, A. Swierczewska-Gwiazda. A note on weak solutions of conservation laws and energy/entropy conservation, arXiv:1706.10154
 

More Information:

For more info contact: Prof. Athanasios Tzavaras: email: athanasios.tzavaras@kaust.edu.sa
 
Date: Tuesday 17th Oct 2017
Time:03:15 PM - 04:15 PM
Location: Location: Building 1, Level 3, Conference room 3422