Related papers: Weakly nonlocal continuum physics - the Ginzburg-L…
The nonlocal field theory commonly requires a minimal length, and so it appears to formulate the nonlocal theory in terms of the doubly special relativity which makes the speed of light and the minimal length invariant simultaneously. We…
Amplitude expansions are used to determine steady states of a semi-infinite solid subject to the Grinfeld instability in systems with a fixed (wave)length. We present two methods to obtain high-order weakly nonlinear results. Using the…
The Ginzburg-Landau equations were proposed in the superconductivity theory to describe mathematically the intermediate state of superconductors in which the normal conductivity is mixed with the superconductivity. It was understood later…
We construct local minimizers to the Ginzburg-Landau functional of superconductivity whose number of vortices N is prescribed and blows up as the parameter epsilon, inverse of the Ginzburg-Landau parameter kappa, tends to zero. We treat the…
The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
We explain how the kinetic theory of L. Boltzmann is applied to weakly nonlinear wave equations.
In this review, we hope to give the reader a self-contained contemporary presentation of the application of Landau theory to ferroelectrics. We begin by developing Landau theory for homogenous bulk ferroelectrics and then consider the…
We introduce the notion of weak containment for stationary actions of a countable group and define a natural topology on the space of weak equivalence classes. We prove that Furstenberg entropy is an invariant of weak equivalence, and…
We examine the procedure of thermodynamical derivation of the Ginsburg--Landau equation for current, which is given unclear and contradictory interpretations in existing textbooks. We clarify all steps of this procedure and find as a…
Non-local elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak non-locality) and the integral non-local models (strong non-locality). This article focuses on the…
The recent discovery that some of the coefficients of the viscosity tensor are negative is shown to invalidate the hydrodynamic approach to the vortex liquid phase of a type-II superconductor. A satisfactory theory requires retention of all…
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the Quantum Energy Inequalities satisfied by…
We investigate a class of nonlocal conservation laws in several space dimensions, where the continuum average of weighted nonlocal interactions are considered over a finite horizon. We establish well-posedness for a broad class of flux…
By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values…
We introduce two different ways of coupling local and nonlocal equations with Neumann boundary conditions in such a way that the resulting model is naturally associated with an energy functional. For these two models we prove that there is…
The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic…
It has been experimentally observed that weakly conducting suspended films of smectic liquid crystals undergo electroconvection when subjected to a large enough potential difference. The resulting counter-rotating vortices form a very…
We consider mixed local and nonlocal quasilinear parabolic equations of $p$-Laplace type and discuss several regularity properties of weak solutions for such equations. More precisely, we establish local boundeness of weak subsolutions,…
The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schr$\ddot{o}$dinger equations on noncommutative(NC) space we obtain the Landau energy levels and the energy correction that is caused by…