Related papers: Schr\"odinger-improved Boussinesq system in two sp…
The Cauchy problem for the inelastic Boltzmann equation is studied for small data. Existence and uniqueness of mild and weak solutions is obtained for sufficiently small data that lies in the space of functions bounded by Maxwellians. The…
We prove almost global existence for supercritical nonlinear Schr\"odinger equations on the $d$-torus ($d$ arbitrary) on the good geometry selected in part I. This is seen as the Cauchy consequence of I, since the known invariant measure of…
In this paper we study the Cauchy problem for the generalized Boussinesq equation with initial data in modulation spaces $M^{s}_{p^\prime,q}(\mathbb{R}^n),$ $n\geq 1.$ After a decomposition of the Boussinesq equation in a $2\times…
We prove existence of a global conservative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line, allowing for nonvanishing and distinct asymptotics at plus and minus infinity. The solution is proven to…
The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering…
We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical…
We shall be concerned with the Cauchy problem for quasilinear systems in three space dimensions of the form \label{i.1} \partial^2_tu^I-c^2_I\Delta u^I = C^{IJK}_{abc}\partial_c u^J\partial_a\partial_b u^K + B^{IJK}_{ab}\partial_a…
We study the Cauchy problem for the nonlinear damped wave equation and establish the large data local well-posedness and small data global well-posedness with slowly decaying initial data. We also prove that the asymptotic profile of the…
The global regularity problem for the Boussinesq system is a well known open problem in mathematical fluid dynamics. As a follow up to our work \cite{EJSI}, we give examples of finite-energy and Lipschitz continuous velocity field and…
We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t^{-1}, whereas the…
This paper is devoted to the analysis of the incompressible Euler equation in a time-dependent fluid domain, whose interface evolution is governed by the law of linear elasticity. Our main result asserts that the Cauchy problem is globally…
We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval $[0,{T}/{\epsilon}]$, for initial data of the form $\epsilon U_0$, where $T$ depends only on…
This paper establishes the global well-posedness of strong solutions to the nonhomogeneous magnetic B\'enard system with positive density at infinity in the whole space $\mathbb{R}^2$. More precisely, we obtain the global existence and…
In this paper, we focus on the existence of strong solutions for the Cauchy problem of the three-dimensional Landau-Lifshitz-Slonczewski equation. We construct a new combination of Bourgain space and Lebesgue space where linear and…
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, the Cauchy problem for the multi-dimensional (M-D) bipolar Euler-Poisson equations with far field vacuum is considered. Based on physical observations and some elaborate analysis of this system's intrinsic symmetric…
The present paper deals with the Cauchy problem of a compressible generic two-fluid model with capillarity effects in any dimension $N\geq2$. We first study the unique global solvability of the model in spaces with critical regularity…
For smooth initial data, we establish the global existence and uniqueness of strong and classical solutions to the Cauchy problem for the barotropic compressible Navier-Stokes equations in two spatial dimensions with vacuum state as far…
For $n\geq 3$, we study the Cauchy problem for the fourth order nonlinear Schr\"{o}dinger equations, for which the existence of the scattering operators and the global well-posedness of solutions with small data in Besov spaces…
We prove that the Cauchy problem for the 2D quintic defocusing biharmonic Schr\"odinger equation is globally well-posed in the Sobolev spaces $H^s(\mathbb{R}^2)$ for $\frac{8}{7}<s<2$. Our main ingredient to establish the result is the…