相关论文: The Cauchy Problem for Dissipative Benjamin-Ono eq…

We consider the well-posedness of the initial value problem associated to the k-generalized Zakharov-Kuznetsov equation in fractional weighted Sobolev spaces. Our method of proof is based on the contraction mapping principle and it mainly…

This paper has various goals: first, we develop a local and global well-posedness theory for the regularized Benjamin-Ono equation in the periodic setting, second, we show that the Cauchy problem for this equation (in both periodic and…

In this article, we examine $L^2$ well-posedness and stabilization property of the dispersion-generalized Benjamin-Ono equation with periodic boundary conditions. The main ingredient of our proof is a development of dissipation-normalized…

We prove the inviscid limit of the incompressible Navier-Stokes equations in the same topology of Besov spaces as the initial data. The proof is based on proving the continuous dependence of the Navier-Stokes equations uniformly with…

In this paper, we study the Cauchy problem for a two-component higher order Camassa-Holm systems with fractional inertia operator $A=(1-\partial_x^2)^r,r\geq1$, which was proposed by Escher and Lyons. By the transport equation theory and…

In this work we prove local and global well-posedness results for the Cauchy problem of a family of regularized nonlinear Benjamin-type equations in both periodic and nonperiodic Sobolev spaces.

We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation.…

We prove that the Cauchy problem for the Schr\"odinger-Korteweg-de Vries system is locally well-posed for the initial data belonging to the Sovolev spaces $L^2(\R)\times H^{-{3/4}}(\R)$. The new ingredient is that we use the $\bar{F}^s$…

Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these models do not propagate polynomial weights of arbitrary magnitude, and the maximum decay rate is…

We consider the Cauchy problem for compressible Navier--Stokes equations of the ideal gas in the three-dimensional spaces. It is known that the Cauchy problem in the scaling critical spaces of the homogeneous Besov spaces $\dot…

The aim of this paper is to prove various ill-posedness and well-posedness results on the Cauchy problem associated to a class of fractional Kadomtsev-Petviashvili (KP) equations including the KP version of the Benjamin-Ono and Intermediate…

The aim of this paper is to investigate well-posedness of the Cauchy problem for the degenerate Zakharov system. Local well-posedness holds for anisotropic Sobolev data by applying $U^2, V^2$ type spaces. We give the Schr\"odinger initial…

We prove existence of a unique global-in-time weak solutions of the Navier-Stokes equations that govern the motion of a compressible viscous fluid with density-dependent viscosity in two-dimensional space. The initial velocity belongs to…

We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted…

We consider the Navier-Stokes Cauchy problem with an initial datum in a weighted Lebesgue space. The weight is a radial function increasing at infinity. Our study partially follows the ideas of the paper by G.P. Galdi and P. Maremonti "On…

In this work we prove that the initial value problem associated to the Schr\"odinger-Benjamin-Ono type system \begin{equation*} \left\{ \begin{array}{ll} \mathrm{i}\partial_{t}u+ \partial_{x}^{2} u= uv+ \beta u|u|^{2},…

We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. The system can be seen as a weak nonlocal dispersive perturbation of the shallow water system. The…

We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space…

We study spatial decay properties for solutions of the Pelinovski-Stepanyants equation posed on the cylinder. We establish the maximum polynomial decay admissible for solutions of such a model. It is verified that the equation on the…

We show that uniqueness results of the kind those obtained for KdV and Schr\"odinger equations ([7], [28]), are not valid for the dispersion generalized-Benjamin-Ono equation in the weighted Sobolev spaces $$H^s(\R)\cap L^2(x^{2r}dx),$$ for…