Rough solutions

The thesis will solve the following two basic objectives: Clarifying the effect of hydrodynamic and geometric factors on the current velocity due to wave at the dike toe by using rocks; Determining the formula to calculate the maximum flow velocity at the foot of the embankment (dike toe), then select the solution to design the structure of the foot protection of the embankment in both with or without roughness structures

27p hobbsandshaw 09-06-2021 14 4   Download

This is the first in a series of papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein-vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. Following [Kl-Ro] we develop new analytic methods based on Strichartz-type inequalities which result in a gain of half a derivative relative to the classical result. ...

52p noel_noel 17-01-2013 61 5   Download

This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. In this paper we develop the geometric analysis of the Eikonal equation for microlocalized rough Einstein metrics. This is a crucial step in the derivation of the decay estimates needed in the first paper. ...

50p noel_noel 17-01-2013 56 5   Download