Related papers: The parabolic flows for complex quotient equations
This article is concerned with developing an analytic theory for second order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an Lp-framework is established by maximal regularity tools. These…
We consider a complex Plateau problem for strongly pseudoconvex contours in non K\"ahler manifolds. A positive solution in the case of manifolds carrying a pluriclosed Hermitian metric forms is given. For the general case we propose a…
We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…
A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments a set of ordinary differential equations are obtained. Successively expanding the…
The applications and impact of high fidelity simulation of fluid flows are far-reaching. They include settling some long-standing and fundamental questions in turbulence. However, the computational resources required for such efforts are…
We consider a family of smooth perturbations of unipotent flows on compact quotients of $\text{SL}(3,\mathbb{R})$ which are not time-changes. More precisely, given a unipotent vector field, we perturb it by adding a non-constant component…
In this paper we first obtain the existence of smooth solutions to Orlicz-Aleksandrov problem via a Gauss-like curvature flow.
This paper defines a parabolic frequency for solutions of the heat equation on a Ricci flow and proves it's monotonicity along the flow. Frequency monotonicity is known to have many useful consequences; here it is shown to provide a simple…
Recently, meshless methods have become popular in numerically solving partial differential equations and have been employed to solve equations governing fluid flows, heat transfer, and species transport. In the present study, a numerical…
We investigate various aspects of a geometric flow defined using the Bach tensor. Firstly, using a well-known split of the Bach tensor components for $(2,2)$ unwarped product manifolds, we solve the Bach flow equations for typical examples…
We introduce a new variational method for finding periodic orbits of flows and spatio-temporally periodic solutions of classical field theories, a generalization of the Newton method to a flow in the space of loops. The feasibility of the…
Here we study the nonlinear hyperbolic equations of the type of equations from theory of flows on networks, for which we prove the solvability theorem under the appropriate conditions and also investigate the behaviour of the solution.
Wegner's method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
The Cahn-Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues. We are interested in quantifying the pressure jump at the interface in the case of incompressible flows. To do so, we…
Based on a comparison principle, we derive an exponential rate of convergence for solutions to the initial-boundary value problem for a class of quasilinear parabolic equations in one space dimension. We then apply the result to some models…
In this paper, complex Hessian equation over K\"ahler manifold was studied. Under the condition that the underline K\"ahler manifold has non-negative holomorphic bisectional curvature, the existence and regularity of the solution was…
We discuss general bosonic configurations of four-dimensional N=2 supergravity coupled to vector multiplets in (t,s) space-time. The supergravity theories with Euclidean and neutral signature are described by the so-called para-special…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover and, in most cases, capitalizing on the resultant group…