  We show that H\"{o}lder continuous incompressible Euler flows that satisfy
the local energy inequality ("globally dissipative" solutions) exhibit
nonuniqueness and contain examples that strictly dissipate kinetic energy. The
collection of such solutions emanating from a fixed initial data may have
positive Hausdorff dimension in the energy space even if the local energy
equality is imposed, and the set of initial data giving rise to such an
infinite family of solutions is $C^0$ dense in the space of continuous,
divergence free vector fields on the torus ${\mathbb T}^3$.
  The construction of these solutions involves a new and explicit convex
integration approach mirroring Kraichnan's LDIA theory of turbulent energy
cascades that overcomes the limitations of previous schemes, which had been
restricted to bounded measurable solutions or to continuous solutions that
dissipate total kinetic energy.
