3 research outputs found
H\"older continuity and differentiability on subsequences
It is shown that an arbitrary function from to will
become -continuous in almost every after restriction to
a certain subset with limit point . For differentiability can be
obtained. Examples show the H\"older exponent is
optimal
Steady and self similar full Euler flow
We consider solutions to the full (non-isentropic) two-dimensional Euler
equations that are constant in time and along rays emanating from the origin.
We prove that for a polytropic equation of state, entropy admissible solutions
in with non-vanishing velocity, density, and internal energy must be
. Moreover, we obtain some results concerning the structure of such
solutions.Comment: 46 pages, 5 figure
Steady and self-similar solutions of non-strictly hyperbolic systems of conservation laws
We consider solutions of two-dimensional systems hyperbolic
conservation laws that are constant in time and along rays starting at the
origin. The solutions are assumed to be small perturbations of a
constant state and entropy admissible, and the system is assumed to be
non-strictly hyperbolic with eigenvalues of constant multiplicity. We show that
such a solution, initially assumed bounded, must be a special function of
bounded variation, and we determine the possible configuration of waves. As a
corollary, we extend some regularity and uniqueness results for some
one-dimensional Riemann problems