arXiv subjects
Publications and source records attributed to Mihaela Ignatova.
We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system in bounded domains, in two dimensions, with Dirichlet boundary conditions for the Navier-Stokes and Poisson equations, and blocking (vanishing normal flux) or selective (Dirichlet) boundary conditions for the ionic concentrations. We prove global existence and stability results for large data.
We prove that the limit of any weakly convergent sequence of Leray-Hopf solutions of dissipative SQG equations is a weak solution of the inviscid SQG equation in bounded domains.
We consider the critical dissipative SQG equation in bounded domains, with the square root of the Dirichlet Laplacian dissipation. We prove global a priori interior $C^α$ and Lipschitz bounds for large data.
We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at $x_2=0$. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has a uniformly integrable tangential gradient near the boundary.
We consider a model of electroconvection motivated by studies of the motion of a two dimensional annular suspended smectic film under the influence of an electric potential maintained at the boundary by two cylindrical electrodes. We prove that this electroconvection model has global in time unique smooth solutions.
We prove nonlinear lower bounds and commutator estimates for the Dirichlet fractional Laplacian in bounded domains. The applications include bounds for linear drift-diffusion equations with nonlocal dissipation and global existence of weak solutions of critical surface quasi-geostrophic equations.
We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted $H^1$ space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within $\varepsilon$ of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time $T_\varepsilon \geq \exp(\varepsilon^{-1}/ \log(\varepsilon^{-1}))$.
We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as formal limits of time discrete pressure-Poisson schemes introduced by Johnston and Liu (J. Comp. Phys. 199 (2004) 221-259) and by Shirokoff and Rosales (J Comp. Phys 230 (2011) 8619-8646) when the initial data does not satisfy the required compatibility condition. Unlike the results of Iyer et al (J. Math. Phys. 53 (2012) 115605), our approach proves existence of weak solutions in domains with less than C^1 regularity. Our approach also addresses uniqueness in 2D and higher regularity.