본문 바로가기
KERD
논문KCI 등재

Existence of strong mild solution of the Navier-Stokes equations in the half space with nondecaying initial data

배형옥|진범자
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회지 (Journal of the KMS)|제49권 제1호|pp. 113-138

2

조회

0

다운로드

2

인용

0

참고문헌

키워드

uniquenessexistenceNavier-Stokesnondecaying data
주제분류수학

초록

We construct a mild solutions of the Navier-Stokes equations in half spaces for nondecaying initial velocities. We also obtain the uniform bound of the velocity field and its derivatives.

Abstract

We construct a mild solutions of the Navier-Stokes equations in half spaces for nondecaying initial velocities. We also obtain the uniform bound of the velocity field and its derivatives.

참고문헌 (17)

  1. H. Amann, "On the strong solvability of the Navier-Stokes equations", J. Math. Fluid Mech, 2(1), pp.16~98 (2000)
  2. H.-O. Bae, "Temporal and spatial decays for the Stokes flow", J. Math. Fluid Mech, 10(4), pp.503~530 (2008)
  3. H.-O. Bae, "Temporal decays in L1 and L1 for the Stokes flow", J. Differential Equations, 222(1), pp.1~20 (2006)
  4. W. Borchers, "L2 decay for the Navier-Stokes flow in halfspaces", Math. Ann, 282(1), pp.139~155 (1988)
  5. F. Crispo, "On the (x; t) asymptotic properties of solutions of the Navier-Stokes equations in the half space", J. Math. Sci, 136(2), pp.3735~3767 (2006)
  6. Y. Fujigaki, "Asymptotic pro les of nonstationary incompressible Navier-Stokes flows in the half-space", Methods Appl. Anal, 8(1), pp.121~157 (2001)
  7. Y. Giga, "Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity", J. Math. Fluid Mech, 3(3), pp.302~315 (2001)
  8. Y. Giga, "On estimates in Hardy spaces for the Stokes ow in a half-space", Math. Z, 231(2), pp.383~396 (1999)
  9. Y. Giga, "Rotating Navier-Stokes equations in R3 + with initial data nondecreasing at in nity: the Ekman boundary layer problem", Arch. Ration. Mech. Anal, 186(2), pp.177~224 (2007)
  10. M. Hieber, "The Navier-Stokes equations in Rn with linearly growing initial data", Arch. Ration. Mech. Anal, 175(2), pp.269~285 (2005)
  11. J. Kato, "The uniqueness of nondecaying solutions for the Navier-Stokes equations", Arch. Ration. Mech. Anal, 169(2), pp.159~175 (2003)
  12. P. Maremonti, "Stokes and Navier-Stokes problems in a half space: the existence and uniqueness of solutions a priori nonconvergent to a limit at infinity", Journal of Mathe- matical Sciences, 159(4), pp.486~523 (2009)
  13. P. Maremonti, "Nonstationary Stokes equations in a half-space with con- tinuous initial data", J. Math. Sci, 127(2), pp.1886~1914 (2005)
  14. E. Nakai, "Generalized Campanato spaces and the uniqueness of nonde- caying solutions for the Navier-Stokes equations", ~ (2009)
  15. Y. Shimizu, "L1 estimate of the first-order space derivatives of Stokes flow in a half space", Funkcial. Ekvac, 42(2), pp.291~309 (1999)
  16. V. A. Solonnikov, "On nonstationary Stokes problem and Navier-Stokes problem in a half- space with initial data nondecreasing at infinity", J. Math. Sci. (N. Y.), 114(5), pp.1726~1740 (2003)
  17. S. Ukai, "A solution formula for the Stokes equation in Rn+, Comm", Pure Appl. Math, 40(5), pp.611~621 (1987)

관련 논문AI추천

NAVIER-STOKES EQUATIONS IN BESOV SPACE B−s ∞,∞(Rn +)진범자대한수학회 · 대한수학회지2013 · 제50권 제4호Regularity of solutions of 3D Navier-Stokes equations in a Lipschitz domain for small data곽민규, 김남권, 정효숙대한수학회 · 대한수학회보2013 · 제50권 제3호Local regularity criteria of the Navier-Stokes equations with slip boundary conditions강경근, 김명현, 배형옥대한수학회 · 대한수학회지2016 · 제53권 제3호New regularity criterion for the Navier-Stokes equationsHu Yue, Yuanshan Zhaoy장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2009 · 제12권 제3호Global existence for 3D Navier-Stokes equations in a long periodic domain곽민규, 김남권대한수학회 · 대한수학회지2012 · 제49권 제2호On the improved regularity criterion of the solutions to the Navier-Stokes equationsSadek Gala대한수학회 · 대한수학회논문집2020 · 제35권 제1호

이 간행물의 다른 논문 (12건)

COVERS OF ALGEBRAIC VARIETIES VI. ANGLO-AMERICAN COVERS AND (1,3)-POLARIZED ABELIAN SURFACESGianfranco Casnatipp. 1-16On boundary regularity of holomorphic correspondencesNabil Ourimipp. 17-30Homological properties of modules over Ding-Chen ringsGang Yangpp. 31-47ℓ-RANKS OF CLASS GROUPS OF FUNCTION FIELDS정환엽, 배성한pp. 49-67Explicit formulas for the Bergman kernel on certain Forelli-Rudin constructionQingbin Li, An Wang, Liyou Zhangpp. 69-83
원문 보기