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We consider a certain three dimensional Euler flow with infinite energy, which is sometimes called the columnar or two and half dimensional flow. We prove the global smoothness of such flow in $\mathbb{R}^3$ when the initial data is in some Sobolev or Besov spaces and $\partial_3 u_3$ is nonnegative.
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참고문헌 (17)
참고문헌 신청
H. Bahouri / 2011 / Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften, 343 / Springer
M. Cannone / Handbook of mathematical fluid dynamics. Vol. III / North-Holland :161~244
D. Chae / 2004 / Local existence and blow-up criterion for the Euler equations in the Besov spaces / Asymptot. Anal. 38(3-4):339~358
P. Constantin / 2000 / The Euler equations and nonlocal conservative Riccati equations / Internat. Math. Res. Notices 2000(9):455~465
R. Danchin / 2005 / Fourier Analysis Methods for PDEs, Lecture Notes
M. Cannone / Handbook of mathematical fluid dynamics. Vol. III / North-Holland :161~244
D. Chae / 2004 / Local existence and blow-up criterion for the Euler equations in the Besov spaces / Asymptot. Anal. 38(3-4):339~358
P. Constantin / 2000 / The Euler equations and nonlocal conservative Riccati equations / Internat. Math. Res. Notices 2000(9):455~465
R. Danchin / 2005 / Fourier Analysis Methods for PDEs, Lecture Notes
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