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This paper is devoted to the study of the weak-strong uniqueness property for full compressible magnetohydrodynamics flows. The governing equations for magnetohydrodynamic flows are expressed by the full Navier-Stokes system for compressible fluids enhanced by forces due to the presence of the magnetic field as well as the gravity and an additional equation which describes the evolution of the magnetic field. Using the relative entropy inequality, we prove that a weak solution coincides with the...
We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over...
An optimal control problem for a model for stationary, low Mach
number, highly nonisothermal, viscous flows is considered.
The control problem involves the minimization of a measure of
the distance between the velocity field and a given target
velocity field. The existence of solutions of a boundary value
problem for the model equations is established as is the
existence of solutions of the optimal control problem. Then, a
derivation of an optimality system, i.e., a boundary value
problem from...
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