Unstable Solutions of the Euler Equations of Certain Variational Problems.
An existence result for partially regular weak solutions of certain abstract evolution equations, with an application to magneto-hydrodynamics.
Einige Bemerkungen zur Frage der eindeutigen Lösbarkeit des Dirichletproblems für ein gewisses System nichtlinearer Differentialgleichungen.
Instabile Flächen vorgeschriebener mittlerer Krümmung.
About an initial-boundary value problem from magneto-hydronamics.
About the Resolvent of an Operator from Fluid Dynamics.
About the Morse Theory for Certain Variational Problems.
Instabile Minimalflächen in Riemannschen Mannigfaltigkeiten nichtpositver Schnittkrümmung.
A remark about a Galerkin method
It is shown that the approximating equations whose existence is required in the author's previous work on partially regular weak solutions can be constructed without any additional assumption about the equation itself. This leads to a variation of a Galerkin method.
Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow
We prove a priori estimates for a linear system of partial differential equations originating from the equations for the flow of a barotropic compressible viscous fluid under the influence of the gravity it generates. These estimates will be used in a forthcoming paper to prove the nonlinear stability of the motionless, spherically symmetric equilibrium states of barotropic, self-gravitating viscous fluids with respect to perturbations of zero total angular momentum. These equilibrium states as...
About the decay of surface waves on viscous fluids without surface tension
We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.
Stationary states and moving planes
Most of the paper deals with the application of the moving plane method to different questions concerning stationary accumulations of isentropic gases. The first part compares the concepts of stationarity arising from the points of view of dynamics and the calculus of variations. Then certain stationary solutions are shown to be unstable. Finally, using the moving plane method, a short proof of the existence of energy-minimizing gas balls is given.
Existence and stability theorems for abstract parabolic equations, and some of their applications
For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.
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