Related papers: A variational approach to the Yau-Tian-Donaldson c…
The following question was proposed by Avi Wigderson and Yuval Wigderson: Is it possible to use the method in their paper(The uncertainty principle: variations on a theme) to prove Heisenberg uncertainty principle in higher dimension R^d,…
We generalise partial results about the Yau-Tian-Donaldson correspondence on ruled manifolds to bundles whose fibre is a classical flag variety. This is done using Chern class computations involving the combinatorics of Schur functors. The…
Aims: To investigate the stability and angular momentum transport by the strato-rotational instability in the nonlinear regime. Methods: The hydrodynamic compressible equations are solved in a cartesian box in which the outer cylinder is…
An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis…
In this paper, we first prove a folklore conjecture on a greatest lower bound of the Calabi energy in all K\"ahler manifold. Similar result in algebriac setting was obtained by S. K. Donaldson. Secondly, we give an upper/lower bound…
Experiments in a modified Taylor-Couette device, spanning Reynolds numbers of $10^5$ to greater than $10^6$, reveal the nonlinear stability of astrophysically-relevant flows. Nearly ideal rotation, expected in the absence of axial…
S. K. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence the normalized Donaldson-Futaki invariants. We answer the question for the Ricci curvature formalism, in place of the scalar curvature. The…
In this article we study the limiting behavior of the K\"ahler Ricci flow on complete non-compact K\"ahler manifolds. We provide sufficient conditions under which a complete non-compact gradient K\"ahler-Ricci soliton is biholomorphic to…
In this work, we prove what appear to be the first Reynolds-semi-robust and pressure-robust velocity error estimates for an H(div)-conforming approximation of unsteady incompressible flows of power-law type fluids. The proposed methods…
In this paper we state the variational principle for the weighted porous media equation. It extends V.I. Arnold's approach to the description of Euler flows as a geodesics on some manifold, i.e. as a critical points of some energy…
We consider the physically relevant fully compressible setting of the Rayleigh Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to the gravitational force. Under suitable restrictions…
In this paper I analyze the onset of Rayleigh-Taylor instability between two linear viscoelastic fluids assuming that the perturbations at the interface are small. In the first half, the paper analyzes a stratified viscoelastic fluid in…
We present upper bounds for the Wasserstein distance of order $p$ between the marginals of L\'evy processes, including Gaussian approximations for jumps of infinite activity. Using the convolution structure, we further derive upper bounds…
We consider the linear stability of dissipative MHD Taylor-Couette flow with imposed toroidal magnetic fields. The inner and outer cylinders can be either insulating or conducting; the inner one rotates, the outer one is stationary. The…
This paper studies the $\tau$-coherence of a (n x p)-observation matrix in a Gaussian framework. The $\tau$-coherence is defined as the largest magnitude outside a diagonal bandwith of size $\tau$ of the empirical correlation coefficients…
The variational approach to weakly nonlocal thermodynamic theories is critically revisited in the light of modern nonequilibrium thermodynamics. The example of Ginzburg-Landau equation is investigated in detail.
The effect of rotation upon the classical two-layer Rayleigh-Taylor instability is considered theoretically and compared with previous experimental results. In particular we consider a two-layer system with an axis of rotation that is…
We consider Borwein-Preiss and Ekeland variational principles using distance functions that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced…
We consider a steady, geophysical 2D fluid in a domain, and focus on its western boundary layer, which is formally governed by a variant of the Prandtl equation. By using the von Mises change of variables, we show that this equation is…
We consider deformations of metrics in a given conformal class such that the smallest eigenvalue of the Ricci tensor to be a constant. It is related to the notion of minimal volumes in comparison geometry. Such a metric with the smallest…