相关论文: Global solution of the initial value problem for t…
We consider a focusing Davey-Stewartson system and construct the solution of the Cauchy problem in the possible presence of exceptional points (and/or curves).
We present a detailed numerical study of various blow-up issues in the context of the focusing Davey-Stewartson II equation. To this end we study Gaussian initial data and perturbations of the lump and the explicit blow-up solution due to…
In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincar\'{e} equations. By choosing a class of new and special initial data, we can transform this d-dimensional Euler-Poincar\'{e} equations into the Camassa-Holm type…
We investigate the Cauchy problem for a 2x2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in R+ x RN. Under appropriate conditions on the exponents and the fractional orders of the time…
In this paper, we prove global well-posedness and scattering of the Cauchy problem for the elliptic-elliptic Davey-Stewartson system (eeDS) for initial data $u_{0}\in L^{2}(\mathbb{R}^{2})$ in the defocusing case and for $u_{0}\in…
We obtain global existence results for the Cauchy problem associated to the Schrodinger-Debye system for a class of data with infinite mass (L2-norm). A smallness condition on data is assumed. Our results include data such as…
We provide a numerical study of various issues pertaining to the dynamics of the Davey-Stewartson systems of the DS II type. In particular we investigate whether or not the properties (blow-up, radiation,...) displayed by the focusing and…
We consider the Cauchy problems in n-dimensional Euclidean space for the plate equation with a weighted L^{1}-initial data. We derive optimal estimates of the L^{2}-norm of solutions for n = 1, 2, 3, 4. In particular, such obtained results…
We study finite time blow-up and global existence of solutions to the Cauchy problem for the porous medium equation with a variable density $\rho(x)$ and a power-like reaction term. We show that for small enough initial data, if…
In this paper we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schr\"odinger equation in $\mathbb{R}^2$ with general data in the critical space $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$. We show that if a…
For periodic initial data with initial density, we establish the global existence and uniqueness of strong and classical solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data…
In this paper, we study the blow-up radial solution of fully parabolic system with higher dimensional two species Cauchy problem for some initial condition. In addition, we show that the set of positive radial functions in…
In this paper, we establish global strong solutions for arbitrarily large initial data to the 2D and 3D compressible Navier-Stokes-Korteweg system, also referred to as the quantum Navier-Stokes equations, originally derived by Dunn and…
The classical solvability of the initial-boundary problem for the Davey-Stewartson-II type system of equations is proved.
We study the global Cauchy problem associated to the Davey-Stewartson system in $\re^n,\ n=2,3$. Existence and uniqueness of solution are stablished for small data in some weak $L^p$ space. We apply an interpolation theorem and the…
This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial…
This paper investigates the Cauchy problem of two-dimensional full compressible Navier-Stokes system with density and temperature vanishing at infinity. For the strong solutions, some a priori weighted $L^2(R^2)$-norm of the gradient of…
We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in $% \mathbb{R}_{+}\times \mathbb{R}^{N}$. Under appropriate conditions on the exponents and the orders of…
We consider the Cauchy problems in the whole space for the wave equation with a weighted L^{1}-initial data. We first derive sharp infinite time blowup estimates of the L^{2}-norm of solutions in the one and two dimensional cases. Then, we…
We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…