On the Well-Posedness of Weak Solutions

On the Well-Posedness of Weak Solutions

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.

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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.

Author Details

Taiping Liu