相关论文: A proof of Einstein's effective viscosity for a di…
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…
An explicit necessary condition for the occurrence of resonance scattering of axial gravitational waves, along with the internal trapping of null geodesics, is proposed for static spherically symmetric perfect fluid solutions to Einstein's…
In this paper, we prove the stabilizability of abstract Parabolic Integro-Differential Equations (PIDE) in a Hilbert space with decay rate $e^{-\gamma t} $ for certain $\gamma > 0,$ by means of a finite dimensional controller in the…
To investigate the attenuation of turbulence in a periodic cube due to the addition of spherical solid particles, we conduct direct numerical simulations using an immersed boundary method with resolving flow around each particle. Numerical…
We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the…
In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…
We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution…
The influence of viscosity on the flow behaviour in spherically symmetric accretion, has been studied here. The governing equation chosen has been the Navier-Stokes equation. It has been found that at least for the transonic solution,…
In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations with a gravitational force and degenerate viscosity coefficients. Under certain assumptions that imposed on the initial data, we…
We present new numerical algorithms for the coupled Einstein-perfect fluid system in axisymmetry. Our framework uses a foliation based on a family of light cones, emanating from a regular center, and terminating at future null infinity.…
We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical…
We consider a microscopic model of spherical particles with inertia in a Stokes flow. As the particle number grows to infinity and their size goes to zero we derive the monokinetic Vlasov-Stokes equations as mean-field limit. We do this…
Motivated by roughness-induced adhesion enhancement (toughening and strengthening) in low modulus materials, we study the detachment of a sphere from a substrate in the presence of both viscoelastic dissipation at the contact edge, and…
The aim of these notes is to present in a comprehensive and relatively self-contained way some recent developments in the mathematical analysis of two-dimensional viscous flows. We consider the incompressible Navier-Stokes equations in the…
In this paper we prove an asymptotic lower bound for the sphere packing density in dimensions divisible by four. This asymptotic lower bound improves on previous asymptotic bounds by a constant factor and improves not just lower bounds for…
A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic stability of the viscous shock wave is established under some smallness conditions. The proof is given by an elementary…
We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an…
The theory of vortex motion in a dilute superfluid of inhomogeneous density demands a boundary layer approach, in which different approximation schemes are employed close to and far from the vortex, and their results matched smoothly…
We interpret the exact solutions previously obtained for spherically symmetric shells of liquid fluid in General Relativity in terms of the energies involved. We show that a certain parameter that was introduced into the solutions by the…
This memoir contains an overview of the proof of the bounded $L^2$ curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the $L^2$-norm of the…