Related papers: The initial value problem for a third-order disper…
We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model…
This paper is devoted to studying the initial value problem for a third-order dispersive equation for closed curves into K\"ahler manifolds. This equation is a geometric generalization of a two-sphere valued system modeling the motion of…
We prove global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation we consider generalizes two-sphere-valued completely integrable systems…
We discuss a short-time existence theorem of solutions to the initial value problem for a fourth-order dispersive flow for curves parametrized by the real line into a compact K\"ahler manifold. Our equations geometrically generalize a…
This paper is concerned with a fourth order nonlinear dispersive partial differential equation for closed curve flow on a K\"ahler manifold. The main results is that the initial value problem has a solution locally in time if the K\"ahler…
We consider a linear second order parabolic system with a third order dispersion term. This type of system arises when considering a nonlinear model equation describing the motion of a vortex filament with axial flow immersed in an…
We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and…
We present a short-time existence theorem of solutions to the initial value problem for Schroedinger maps of a closed Riemannian manifold to a compact almost Hermitian manifold. The classical energy method cannot work for this problem since…
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…
We study the well-posedness of the initial value problem on periodic intervals for linear and quasilinear evolution equations for which the leading-order terms have three spatial derivatives. In such equations, there is a competition…
We study an evolution problem in the space of continuous loops in three-dimensional Euclidean space modelled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting…
In this paper, we discuss initial-boundary value problems for linear diffusion equation with multiple time-fractional derivatives. By means of the Mittag-Leffler function and the eigenfunction expansion, we reduce the problem to an integral…
A fourth-order dispersive flow equation for closed curves on the canonical two-dimensional unit sphere arises in some contexts in physics and fluid mechanics. In this paper, a geometric generalization of the sphere-valued model is…
In this paper, we consider the initial-boundary value problem of three-dimensional isentropic compressible Navier-Stokes equations with rotating effect terms in an exterior domain with Navier-slip boundary condition and with far-field…
This paper investigates the initial value problem for a system of one-dimensional fourth-order dispersive partial differential-integral equations with nonlinearity involving derivatives up to second order. Examples of the system arise in…
In this paper, we investigate the well-posedness and the long-time asymptotic behavior for the initial-boundary value problem for multi-term time-fractional diffusion equations, where the time differentiation consists of a finite summation…
We study initial value problem for a system consisting of an integer order and distributed-order fractional differential equation describing forced oscillations of a body attached to a free end of a light viscoelastic rod. Explicit form of…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…
Symplectic geometry of the vortex filament in a curved three-manifold is investigated. There appears an infinite sequence of constants of motion in involution in the case of constant curvature. The Duistermaat-Heckman formula is examined…