TY - JOUR
T1 - On the nonlinear instability of euler and prandtl equations
AU - Grenier, Emmanuel
PY - 2000/9
Y1 - 2000/9
N2 - In this paper we give examples of nonlinearly unstable solutions of Euler equations in the whole space ℝ2, the half space ℝ x ℝ+, the periodic strip ℝ x double-struck T sign, the strip ℝ x [-1, 1], and the periodic torus double-struck T sign2, with an application to vortex sheets. Using the same methods, we prove an instability result for Prandtl-type boundary layers that appear in ℝ x ℝ+ and double-struck T sign x ℝ+.
AB - In this paper we give examples of nonlinearly unstable solutions of Euler equations in the whole space ℝ2, the half space ℝ x ℝ+, the periodic strip ℝ x double-struck T sign, the strip ℝ x [-1, 1], and the periodic torus double-struck T sign2, with an application to vortex sheets. Using the same methods, we prove an instability result for Prandtl-type boundary layers that appear in ℝ x ℝ+ and double-struck T sign x ℝ+.
UR - https://www.scopus.com/pages/publications/0034403210
U2 - 10.1002/1097-0312(200009)53:9<1067::AID-CPA1>3.0.CO;2-Q
DO - 10.1002/1097-0312(200009)53:9<1067::AID-CPA1>3.0.CO;2-Q
M3 - Article
AN - SCOPUS:0034403210
SN - 0010-3640
VL - 53
SP - 1067
EP - 1091
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 9
ER -