TY - JOUR
T1 - Large time behavior of solutions to the 3D anisotropic Navier–Stokes equation
AU - Fujii, Mikihiro
N1 - Funding Information:
This work was partly supported by Grant-in-Aid for JSPS Research Fellow, Japan , Grant Number JP20J20941 . 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.
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2023/6
Y1 - 2023/6
N2 - We consider the large time behavior of the solution to the 3D Navier–Stokes equation with horizontal viscosity Δhu=∂12u+∂22u and show that the Lp decay rate of the horizontal components of the velocity field coincides to that of the 2D heat kernel, while the vertical component decays like the 3D heat kernel. Moreover, we consider the asymptotic expansion of the solution and find that a portion of the nonlinear term affect the leading term of the horizontal components of the velocity field, whereas the leading term of the vertical component is given by only the linear solution.
AB - We consider the large time behavior of the solution to the 3D Navier–Stokes equation with horizontal viscosity Δhu=∂12u+∂22u and show that the Lp decay rate of the horizontal components of the velocity field coincides to that of the 2D heat kernel, while the vertical component decays like the 3D heat kernel. Moreover, we consider the asymptotic expansion of the solution and find that a portion of the nonlinear term affect the leading term of the horizontal components of the velocity field, whereas the leading term of the vertical component is given by only the linear solution.
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U2 - 10.1016/j.nonrwa.2022.103821
DO - 10.1016/j.nonrwa.2022.103821
M3 - Article
AN - SCOPUS:85145651897
SN - 1468-1218
VL - 71
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
M1 - 103821
ER -