On the Navier-Stokes Equations in Non-Cylindrical Domains: On the Existence and Regularity.
On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion
This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in R³ with C³ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter λ → 0. Moreover, the existence of L²-strong solution, in the small, and in the large for small data, is proved. Asymptotic regularity (the regularity after a finite period) of a weak solution is studied. Finally, using the Dore-Venni theory,...
Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains
In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence...
The equations of viscous incompressible nonhomogeneous fluids in noncylindrical domains: on the existence and regularity
We prove the existence of a weak solution and of a strong solution (locally in time) of the equations which govern the motion of viscous incompressible non-homogeneous fluids. Then we discuss the decay problem.
On the existence of weak solutions of a nonlinear mixed problem for nonhomogeneous fluids in a time dependent domain
On the existence of weak solutions of boundary value problems in a diffusion model for an inhomogeneous liquid in regions with moving boundaries
Some problems of vector analysis in solenoidal spaces
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