相关论文: Loss of Regularity of Solutions to Shock Reflectio…
Vortices (flows with closed elliptic streamlines) are exact nonlinear solutions to the compressible Euler equation. In this contribution, we use differential geometry to derive the transformations between Cartesian and elliptic coordinates,…
We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas. We prove that the well-known phenomenon of shock formation in simple…
We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of…
An analytical solution for high supersonic flow over a circular cylinder based on Schneider's inverse method has been presented. In the inverse method, a shock shape is assumed and the corresponding flow field and the shape of the body…
Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…
The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressible flow of an ideal fluid whose Lagrangian transport…
We consider the problem of shock reflection on a solid wall in plane symmetry for a barotropic fluid. We establish a local in time solution after the point of reflection, thereby determining the state behind the reflected shock. The…
We establish the equivalence of free piston and delta shock, for the one-space-dimensional pressureless compressible Euler equations. The delta shock appearing in the singular Riemann problem is exactly the piston that may move freely…
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…
We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough…
We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest. When the shock impinges on the density discontinuity, it refracts and in the hydrodynamical case 3 signals arise.…
We formulated a problem on hypersonic limit of two-dimensional steady non-isentropic compressible Euler flows passing a straight wedge. It turns out that Mach number of the upcoming uniform supersonic flow increases to infinite may be taken…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
This paper investigates the nonlinear dynamics of Newton's problem of minimal resistance in radial fields. We move beyond classical translational symmetry to analyze two non-equilibrium scenarios: a scale-invariant free expansion and an…
We consider self-similar potential flow for compressible gas with polytropic pressure law. Self-similar solutions arise as large-time asymptotes of general solutions, and as exact solutions of many important special cases like Mach…
We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…
We consider self-similar solutions to the full compressible Euler system for an ideal gas in two and three space dimensions. The system admits a 2-parameter family of similarity solutions depending on parameters $\lambda$ and $\kappa$.…
A basic example of shear flow was introduced by DiPerna and Majda to study the weak limit of oscillatory solutions of the Euler equations of incompressible ideal fluids. In particular, they proved by means of this example that weak limit of…
The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the…
We discuss different notions of continuous solutions to the balance law \[u_t + (f(u ))_x =g \] with $g$ bounded, $f\in C^{2}$, extending previous works relative to the flux $f(u)=u^{2}$. We establish the equivalence among distributional…