TY - JOUR
T1 - On the Well-Posedness of Weak Solutions
AU - Liu , Taiping
JO - Annals of Applied Mathematics
VL - 3
SP - 309
EP - 316
PY - 2020
DA - 2020/08
SN - 35
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/18084.html
KW - nonlinear partial differential equations, well-posedness theory, weak solutions.
AB - <p style="text-align: justify;">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.</p>