On the uniqueness of bounded weak solutions to the Navier-Stokes Cauchy problem
On the uniqueness of weak solutions for the 3D Navier-Stokes equations
On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients
We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution....
On weak solutions of the equations of motion of a viscoelastic medium with variable boundary.
On weak-strong uniqueness property for full compressible magnetohydrodynamics flows
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...
Optimal interior partial regularity for nonlinear elliptic systems for the case under natural growth condition.