TY - JOUR
T1 - Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation
AU - Fujii, Mikihiro
N1 - Funding Information:
The author would like to express his sincere gratitude to Professor Jun-ichi Segata, Faculty of Mathematics, Kyushu University, for many fruitful advices and continuous encouragement. This work was partly supported by Grant-in-Aid for JSPS Research Fellow Grant Number JP20J20941.
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.
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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 -