Related papers: Global weak solutions for a two-component Novikov …
In this paper, we consider the existence of global weak solutions to a one dimensional fluid-particles interaction model: inviscid Burgers-Vlasov equations with fluid velocity in $L^\infty$ and particles' probability density in $L^1$. Our…
We consider the global existence and scattering for solutions of magnetic Zakharov system in three-dimensional space. When the initial data is small, we prove the existence of smooth global solutions and scattering results, by combining the…
This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatment of variable singular exponents alongside measure-valued…
The purpose of this note is to study the weak solutions to the inviscid quasi-geostrophic system for initial data belonging to Lebesgue spaces. We give a global existence result as well as detail the connections between several different…
Our interest itself of this paper is strongly inspired from an open problem in the paper [1] published by D'Abbicco. In this article, we would like to study the Cauchy problem for a weakly coupled system of semi-linear structurally damped…
In this paper, we shall prove the global existence of weak solutions to 3D inhomogeneous incompressible Navier-Stokes system $({\rm INS})$ with initial density in the bounded function space and having a positive lower bound and with initial…
We consider a full Navier-Stokes and $Q$-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly…
We study the global existence of solutions to a two-component generalized Hunter-Saxton system in the periodic setting. We first prove a persistence result of the solutions. Then for some particular choices of parameters $(\alpha, \kappa)$,…
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N=2. We address the question of the global existence of strong solutions with large initial data for compressible Navier-Stokes system and Korteweg…
We apply ideas from viscosity theory to establish the existence of a unique global weak solution to the generalized Kahler-Ricci flow in the setting of commuting complex structures. Our results are restricted to the case of a smooth…
The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the…
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…
The global-in-time existence of weak solutions to a spatially homogeneous multispecies Fokker-Planck-Landau system for plasmas in the three-dimensional whole space is shown. The Fokker-Planck-Landau system is a simplification of the Landau…
In this paper, we investigate existence of global-in-time strong solutions to the kinetic Cucker--Smale model coupled with the Stokes equations in the whole space. By introducing a weighted Sobolev space and using space-time estimates for…
We consider a Stokes-Magneto system in $\mathbb{R}^d$ ($d\geq 2$) with fractional diffusions $\Lambda^{2\alpha}\boldsymbol{u}$ and $\Lambda^{2\beta}\boldsymbol{b}$ for the velocity $\boldsymbol{u}$ and the magnetic field $\boldsymbol{b}$,…
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…
In this note we give a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data.
We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen--Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The…
In this paper we established the global well-posedness theorem for a special type of wave-Klein-Gordon system that have the strong coupling terms in divergence form on the right hand side of its wave equation. We cope with the problem by…
The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…