Related papers: Global classical solutions to the compressible Eul…
We examine the two-dimensional Euler equations including the local energy (in)equality as a differential inclusion and show that the associated relaxation essentially reduces to the known relaxation for the Euler equations considered…
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…
A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the…
Energy conservations are studied for inhomogeneous incompressible and compressible Euler equations with general pressure law in a torus or a bounded domain. We provide sufficient conditions for a weak solution to conserve the energy. By…
In this paper, the smooth solution of the physical vacuum problem for the one dimensional compressible Euler equations with time-dependent damping is considered. Near the vacuum boundary, the sound speed is $C^{1/2}$-H\"{o}lder continuous.…
In this paper we study the existence of global-in-time energy solutions to the Cauchy problem for the Euler-Poisson-Darboux equation, with a power nonlinearity: $$u_{tt}-u_{xx} + \frac\mu{t}\,u_t = |u|^p \,, \quad t>t_0, \…
By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion…
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in three spatial dimensions with smooth initial data which are of small energy but…
In this paper, for compressible Euler equations in multiple space dimensions, we prove the break-down of classical solutions with a large class of initial data by tracking the propagation of radially symmetric expanding wave including…
Solutions to a class of conservation laws with discontinuous flux are constructed relying on the Crandall-Liggett theory of nonlinear contractive semigroups~\cite{CL}. In particular, the paper studies the existence of backward Euler…
This paper aims to incorporate the Caflisch's decomposition into the macro-micro decomposition in Boltzmann theory for allowing the microscopic component to exhibit only the polynomial tail in large velocities. In particular, we treat the…
We study the large-time asymptotic behavior of solutions to the one-dimensional damped pressureless Euler-Poisson system with variable background states, subject to a neutrality condition. In the case where the background density converges…
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…
In this paper, we study the Cauchy's problem of the compressible Euler system with damping and establish the global-in-time well-posedness in $L^p$-type critical Besov spaces for $1\leq p<2$. To achieve it, a new product estimate is…
Compressible Euler-Poisson equations are the standard self-gravitating models for stellar dynamics in classical astrophysics. In this article, we construct periodic solutions to the isothermal ($\gamma=1$) Euler-Poisson equations in $R^{2}$…
We consider the Cauchy problem of massless Dirac-Maxwell equations on an asymptotically flat background and give a global existence and uniqueness theorem for initial values small in an appropriate weighted Sobolev space. The result can be…
In this paper, the compressible Euler system with velocity alignment and damping is considered, where the influence matrix of velocity alignment is not positive definite. Sound speed is used to reformulate the system into symmetric…
In this paper, the global well-posedness and stability of classical solutions to the multidimensional hydrodynamic model for semiconductors on the framework of Besov space are considered. We weaken the regularity requirement of the initial…
This paper studies an initial boundary value problem for the multidimensional hyperbolized compressible Navier-Stokes equations, in which the classical Newtonian law is replaced by the Maxwell law. We seek spherically symmetric solutions to…
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…