Related papers: Stokes matrices for Airy equations

In this paper, we consider the generalized stationary Stokes system with $p$-growth and Dini-$\operatorname{BMO}$ regular coefficients. The main purpose is to establish pointwise estimates for the shear rate and the associated pressure to…

Recently, a remarkable correspondence has been unveiled between a certain class of ordinary linear differential equations (ODE) and integrable models. In the first part of the report, we survey the results concerning the 2nd order…

We propose a Lie-theoretic definition of the tt*-Toda equations for any complex simple Lie algebra $\mathfrak{g}$, based on the concept of topological-antitopological fusion which was introduced by Cecotti and Vafa. Our main result concerns…

In this paper we study the map associating to a linear differential operator with rational coefficients its monodromy data. The operator has one regular and one irregular singularity of Poincare' rank 1. We compute the Poisson structure of…

We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the…

We consider a continuous analogue of Babai et al.'s and Cai et al.'s problem of solving multiplicative matrix equations. Given $k+1$ square matrices $A_{1}, \ldots, A_{k}, C$, all of the same dimension, whose entries are real algebraic, we…

We consider the category of perverse sheaves on a complex vector space smooth with respect to a stratification given by an arrangement of hyperplanes with real equations. As shown in an earlier wotk of two of the authors, this category can…

This paper establishes global weighted Calder\'on-Zygmund type regularity estimates for weak solutions of a class of generalized Stokes systems in divergence form. The focus of the paper is on the case that the coefficients in the…

We consider a second order reducible equation having non-resonant irregular singularities at $x=0$ and $x=\infty$. Both of them are of Poincar\'{e} rank 1. We introduce a small complex parameter $\varepsilon$ that splits together $x=0$ and…

Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…

The local analytic classification of irregular linear q-difference equations has recently been obtained by J.-P. Ramis, J. Sauloy and C. Zhang. Their description involves a q-analog of the Stokes sheaf and theorems of Malgrange-Sibuya type…

We produce a new proof of Tao's result on the slightly supercritical Navier Stokes equations. Our proof has the advantage that it works in the plane while Tao's proof works only in dimensions three and higher. We accomplish this by studying…

We consider traveling waves on a surface of an ideal fluid of finite depth. The equation describing Stokes waves in conformal variables formulation are referred to as the Babenko equation. We use a Newton-Conjugate-Gradient method to…

There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…

Recently, Dorey and Tateo have investigated functional relations among Stokes multipliers for a Schr{\"o}dinger equation (second order differential equation) with a polynomial potential term in view of solvable models. Here we extend their…

In this paper we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to…

Let A be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P^1 with values in the Hall algebra of A. The…

We prove the conjectural relation between the Stokes matrix for the quantum cohomology and an exceptional collection generating the derived category of coherent sheaves in the case of the Grassmannian. The proof is based on the relation…

We consider the steady Stokes equations in a bounded domain with forcing in divergence form supplemented with no-slip boundary conditions. We provide a maximal regularity theory in Campanato spaces (inlcuding $\mathrm{BMO}$ and…

In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…