Related papers: Unique equilibrium states for Viana maps with smal…
We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for H\"older potentials satisfying the pressure gap condition. In addition, we provide a criterion for a continuous potential to satisfy the…
In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold, and that they are stable under…
We study the existence, uniqueness, and stability of self-similar expanders of the harmonic map heat flow in equivariant settings. We show that there exist selfsimilar solutions to any admissiable initial data and that their uniqueness and…
This paper is concerned with singular shocks for a system of conservation laws modeling incompressible two-phase fluid flow. We prove the existence of viscous profiles using the Geometric Singular Perturbation Theory. Weak convergence and…
We examine the question of uniqueness for the equivariant reduction of the harmonic map heat flow in the energy supercritical dimension. It is shown that, generically, singular data can give rise to two distinct solutions which are both…
In this paper, we first study the $\alpha-$energy functional, Euler-Lagrange operator and $\alpha$-stress energy tensor. Second, it is shown that the critical points of $\alpha-$ energy functional are explicitly related to harmonic maps…
Let $f:I \to I$ be a $C^2$ multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential $\phi_t:x\mapsto -t\log|Df(x)|$ for $t$…
Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics [10,11,12,16] is extended to the case of temperature-dependent surface tension. We prove well-posedness in an Lp-setting,…
A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently…
We demonstrate existence in the ``large" and uniqueness in the ``small" of equilibrium configurations for the coupled system consisting of a Navier-Stokes fluid interacting with a rigid body subjected to spring forces and restoring moments.…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line…
We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier-Stokes equations with evolutionary equations for the deformation…
In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground…
In this thesis, I study a two-dimensional extended Hubbard model in the weak coupling limit. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons. However in the special case of a…
Gapless superconductivity can arise when pairing occurs between fermion species with different Fermi surface sizes, provided there is a sufficiently large mismatch between Fermi surfaces and/or at sufficiently large coupling constant. In…
First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…
We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…
We study the occurrence of limit cycles from a point on the discontinuity hyperplane $L$ between two smooth vector fields where the two vector fields both point towards one another. Generically, such a point (called switched equilibrium in…
The problem of regularity and uniqueness are open for the supercritically dissipative surface quasi-geostrophic equations in certain classes. In this note we examine the extent to which small or large scales are necessarily active both for…