Related papers: Non-existence and Non-uniqueness for Multidimensio…
In the spirit of D. Hoff's weak solution theory for the compressible Navier-Stokes equations (CNS) with bounded density, in this paper we establish the global existence and regularity properties of finite-energy weak solutions to an initial…
We show the short time existence and uniqueness of solutions to the Cauchy problem for fully nonlinear systems of arbitrary even order on closed manifolds which are strongly parabolic at the initial values. The proof uses a linearization…
The existence and uniqueness of the global strong solution with small initial data to the three-dimensional viscoelastic fluids is established.
In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
In this paper, we study the global existence of solutions of the Cauchy problem for a class of weakly dissipative nonlinear dispersive wave equations…
We show existence of a global weak dissipative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second component in the 2CH…
We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…
The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained. The proofs are based…
The Cauchy problem for nonlinear elastic wave equations with viscoelastic damping terms is investigated in $L^{p}$ framework. It is proved that the small global solutions constructed in $L^{2}$-Sobolev spaces in our preceding paper [12]…
In this paper we study the problem of the global existence (in time) of weak, entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models the dynamics of phase…
The limiting case of the system of equations of two-dimensional gas dynamics in the presence of the Coriolis force, which can be obtained under the assumption of a small pressure, is considered. With this approach, the equation for the…
The nonhomogeneous incompressible Magnetohydrodynamic Equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with slip boundary conditions. The key is the constraint of an additional initial value…
The existence of solutions to Cauchy type problems of linear Riemann-Liouville fractional differential equations with variable coefficients is considered in a space of integrable functions. First, we consider the existence and uniqueness of…
In this paper, we consider the Cauchy problem to the heat conductive compressible Navier-Stokes equations in the presence of vacuum and with vacuum far field. Global well-posedness of strong solutions is established under the assumption,…
In this paper, we consider the Cauchy problem of the multi-dimensional compressible Navier-Stokes-Euler system for two-phase flow motion, which consists of the isentropic compressible Navier-Stokes equations and the isothermal compressible…
In this paper we propose a new approach to prove the local well-posedness of the Cauchy problem associated with strongly non resonant dispersive equations. As an example we obtain unconditional well-posedness of the Cauchy problem below $…
This paper studies a space-inhomogeneous Boltzmann-Nordheim equation with pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem in a setting with large bounded L1 initial data. The main results are existence,…
We prove the existence of a weak solution to the equations describing the inertial motions of a coupled system constituted by a rigid body containing a viscous compressible fluid. We then provide a weak-strong uniqueness result that allows…
This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic…