Godin studies two-dimensional compressible Euler flow in bounded impermeable domains with a boundary that is smooth except for corners. Assuming that the angles of the corners are small enough, he obtains local (in time) existence of solutions that keep the L2 Sobolev regularity of the Cauchy data, provided the external forces are sufficiently regular and suitable compatibility conditions are satisfied. Such a result is well known in cases with no corner, he says, and his proof relies on the study of associated linear problems. He also shows that his results are rather sharp: he constructs counter-examples in which the smallness condition of the angles is not fulfilled, and so display a loss of L2 Sobolev regularity with respect to the Cauchy data and the external forces. Annotation ©2021 Ringgold, Inc., Portland, OR (protoview.com)
