Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces.
Perturbative methods in scales of Banach spaces: applications for Gevrey regularity of solutions to semilinear partial differential equations.
Planar flows of incompressible heat-conducting shear-thinning fluids — existence analysis
We study the flow of an incompressible homogeneous fluid whose material coefficients depend on the temperature and the shear-rate. For large class of models we establish the existence of a suitable weak solution for two-dimensional flows of fluid in a bounded domain. The proof relies on the reconstruction of the globally integrable pressure, available due to considered Navier’s slip boundary conditions, and on the so-called -truncation method, used to obtain the strong convergence of the velocity...
Positive solution for the elliptic problems with sublinear and superlinear nonlinearities.