TY - JOUR
T1 - Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation
AU - Fujii, Mikihiro
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2022/3
Y1 - 2022/3
N2 - We consider the 2D dissipative quasi-geostrophic equation with the time periodic external force and prove the existence of a unique time periodic solution in the case of the supercritical dissipation. In this case, the smoothing effect of the semigroup generated by the dissipation term is too weak to control the nonlinearity in the Duhamel term of the corresponding integral equation. In this paper, we give a new approach which does not depend on the contraction mapping principle for the integral equation.
AB - We consider the 2D dissipative quasi-geostrophic equation with the time periodic external force and prove the existence of a unique time periodic solution in the case of the supercritical dissipation. In this case, the smoothing effect of the semigroup generated by the dissipation term is too weak to control the nonlinearity in the Duhamel term of the corresponding integral equation. In this paper, we give a new approach which does not depend on the contraction mapping principle for the integral equation.
KW - Energy estimates
KW - The 2D dissipative quasi-geostrophic equations
KW - Time periodic solution
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U2 - 10.1007/s00028-022-00787-6
DO - 10.1007/s00028-022-00787-6
M3 - Article
AN - SCOPUS:85126255956
SN - 1424-3199
VL - 22
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 1
M1 - 24
ER -