Year: 2019
Author: Taiping Liu
Annals of Applied Mathematics, Vol. 35 (2019), Iss. 3 : pp. 309–316
Abstract
This is to comment on the well-posedness of weak solutions for the initial value problem for partial differential equations. In recent decades, and particularly in recent years, there have been substantial progresses on construction by convex integration for the study of non-uniqueness of solutions for incompressible Euler equations, and even for compressible Euler equations. This prompts the question of whether it is possible to give a sense of well-posedness, which is narrower than the canonical Hadamard sense, so that the evolutionary equations are well-posed. We give a brief and partial review of the related results and offer some thoughts on this fundamental topic.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-AAM-18084
Annals of Applied Mathematics, Vol. 35 (2019), Iss. 3 : pp. 309–316
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: nonlinear partial differential equations well-posedness theory weak solutions.