Special Session 27: Recent Trends in Navier-Stokes Equations, Euler Equations, and Related Problems

On well-posedness of quantum fluid systems in the class of dissipative solutions

Tong Tang
Yangzhou University
Peoples Rep of China
Co-Author(s):    Danica Basari\`{c}
Abstract:
The main objects of the present work are the quantum Navier--Stokes and quantum Euler systems; for the first one, in particular, we will consider constant viscosity coefficients. We deal with the concept of dissipative solutions, for which we will first prove the weak-strong uniqueness principle and afterwards, we will show the global existence for any finite energy initial data. Finally, we will prove that both systems admit a semiflow selection in the class of dissipative solutions.