TY - JOUR
T1 - Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation
AU - Ferreira, Lucas C.F.
AU - Carrillo, José A.
PY - 2007/6/1
Y1 - 2007/6/1
N2 - We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. While the only small self-similar solution in the strong ℒp space is the null solution, infinitely many self-similar solutions do exist in weak- ℒp spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained. © Springer-Verlag 2007.
AB - We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. While the only small self-similar solution in the strong ℒp space is the null solution, infinitely many self-similar solutions do exist in weak- ℒp spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained. © Springer-Verlag 2007.
KW - Self-similar solutions
KW - Long time asymptotics
KW - Quasi-geostrophic equation
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=2327237
U2 - 10.1007/s00605-007-0447-7
DO - 10.1007/s00605-007-0447-7
M3 - Article
SN - 0026-9255
VL - 151
SP - 111
EP - 142
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
ER -