메뉴 건너뛰기




Volumn 226, Issue 2, 2006, Pages 594-618

Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary

Author keywords

Boundary regularity; Navier Stokes equations; Suitable weak solution

Indexed keywords


EID: 33646520121     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2005.12.007     Document Type: Article
Times cited : (37)

References (32)
  • 1
    • 84990576577 scopus 로고
    • Partial regularity of suitable weak solutions of the Navier-Stokes equations
    • Caffarelli L., Kohn R., and Nirenberg L. Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math. 35 (1982) 771-831
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 771-831
    • Caffarelli, L.1    Kohn, R.2    Nirenberg, L.3
  • 2
    • 0035511536 scopus 로고    scopus 로고
    • Morrey space techniques applied to the interior regularity problem of the Navier-Stokes equations
    • Chen Z.-M., and Price W.G. Morrey space techniques applied to the interior regularity problem of the Navier-Stokes equations. Nonlinearity 14 6 (2001) 1453-1472
    • (2001) Nonlinearity , vol.14 , Issue.6 , pp. 1453-1472
    • Chen, Z.-M.1    Price, W.G.2
  • 3
    • 0001255802 scopus 로고    scopus 로고
    • On the singular set in the Navier-Stokes equations
    • Choe H., and Lewis J.L. On the singular set in the Navier-Stokes equations. J. Funct. Anal. 175 2 (2000) 348-369
    • (2000) J. Funct. Anal. , vol.175 , Issue.2 , pp. 348-369
    • Choe, H.1    Lewis, J.L.2
  • 4
    • 0042597993 scopus 로고    scopus 로고
    • 3, ∞-solutions of Navier-Stokes equations and backward uniqueness
    • (in Russian); translation from Russian in
    • 3, ∞-solutions of Navier-Stokes equations and backward uniqueness. Uspekhi Mat. Nauk 58 2(350) (2003) 3-44 (in Russian); translation from Russian in
    • (2003) Uspekhi Mat. Nauk , vol.58 , Issue.2 350 , pp. 3-44
    • Escauriaza, L.1    Seregin, G.2    Šverák, V.3
  • 5
    • 0042154193 scopus 로고    scopus 로고
    • 3, ∞-solutions of Navier-Stokes equations and backward uniqueness
    • 3, ∞-solutions of Navier-Stokes equations and backward uniqueness. Math. Surveys 58 2 (2003) 211-250
    • (2003) Math. Surveys , vol.58 , Issue.2 , pp. 211-250
    • Escauriaza, L.1    Seregin, G.2    Šverák, V.3
  • 7
    • 46149140458 scopus 로고
    • p and regularity of weak solutions of the Navier-Stokes system
    • p and regularity of weak solutions of the Navier-Stokes system. J. Differential Equations 62 2 (1986) 186-212
    • (1986) J. Differential Equations , vol.62 , Issue.2 , pp. 186-212
    • Giga, Y.1
  • 8
    • 0002460928 scopus 로고
    • p estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
    • p estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains. J. Funct. Anal. 102 (1991) 72-94
    • (1991) J. Funct. Anal. , vol.102 , pp. 72-94
    • Giga, Y.1    Sohr, H.2
  • 9
    • 84944818416 scopus 로고
    • Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen
    • Hopf E. Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4 (1951) 213-231
    • (1951) Math. Nachr. , vol.4 , pp. 213-231
    • Hopf, E.1
  • 10
    • 8744221345 scopus 로고    scopus 로고
    • On boundary regularity of the Navier-Stokes equations
    • Kang K. On boundary regularity of the Navier-Stokes equations. Comm. Partial Differential Equations 29 7-8 (2004) 955-987
    • (2004) Comm. Partial Differential Equations , vol.29 , Issue.7-8 , pp. 955-987
    • Kang, K.1
  • 12
    • 0013198034 scopus 로고    scopus 로고
    • On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations
    • Ladyzenskaja O.A., and Seregin G.A. On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations. J. Math. Fluid Mech. 1 (1999) 356-387
    • (1999) J. Math. Fluid Mech. , vol.1 , pp. 356-387
    • Ladyzenskaja, O.A.1    Seregin, G.A.2
  • 13
    • 51249193194 scopus 로고
    • Sur le mouvement d'un liquide visqueux emplissant l'espace
    • Leray J. Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 64 (1934) 193-248
    • (1934) Acta Math. , vol.64 , pp. 193-248
    • Leray, J.1
  • 14
    • 0032344639 scopus 로고    scopus 로고
    • A new proof of the Caffarelli-Kohn-Nirenberg theorem
    • Lin F. A new proof of the Caffarelli-Kohn-Nirenberg theorem. Comm. Pure Appl. Math. 51 3 (1998) 241-257
    • (1998) Comm. Pure Appl. Math. , vol.51 , Issue.3 , pp. 241-257
    • Lin, F.1
  • 15
    • 0001654863 scopus 로고    scopus 로고
    • On Leray's self-similar solutions of the Navier-Stokes equations
    • Nečas J., Růžička M., and Šverák V. On Leray's self-similar solutions of the Navier-Stokes equations. Acta Math. 176 2 (1996) 283-294
    • (1996) Acta Math. , vol.176 , Issue.2 , pp. 283-294
    • Nečas, J.1    Růžička, M.2    Šverák, V.3
  • 16
    • 0001307388 scopus 로고
    • Un teorema di unicita per le equazioni di Navier-Stokes
    • (in Italian)
    • Prodi G. Un teorema di unicita per le equazioni di Navier-Stokes. Ann. Mat. Pura Appl. (4) 48 (1959) 173-182 (in Italian)
    • (1959) Ann. Mat. Pura Appl. (4) , vol.48 , pp. 173-182
    • Prodi, G.1
  • 17
    • 84972517978 scopus 로고
    • Partial regularity of solutions to the Navier-Stokes equations
    • Scheffer V. Partial regularity of solutions to the Navier-Stokes equations. Pacific J. Math. 66 2 (1976) 535-552
    • (1976) Pacific J. Math. , vol.66 , Issue.2 , pp. 535-552
    • Scheffer, V.1
  • 18
    • 0002117826 scopus 로고
    • Hausdorff measure and the Navier-Stokes equations
    • Scheffer V. Hausdorff measure and the Navier-Stokes equations. Comm. Math. Phys. 55 (1977) 97-112
    • (1977) Comm. Math. Phys. , vol.55 , pp. 97-112
    • Scheffer, V.1
  • 19
    • 0001881423 scopus 로고
    • The Navier-Stokes equations on a bounded domain
    • Scheffer V. The Navier-Stokes equations on a bounded domain. Comm. Math. Phys. 73 1 (1980) 1-42
    • (1980) Comm. Math. Phys. , vol.73 , Issue.1 , pp. 1-42
    • Scheffer, V.1
  • 20
    • 0043106636 scopus 로고
    • Boundary regularity for the Navier-Stokes equations in a half-space
    • Scheffer V. Boundary regularity for the Navier-Stokes equations in a half-space. Comm. Math. Phys. 85 2 (1982) 275-299
    • (1982) Comm. Math. Phys. , vol.85 , Issue.2 , pp. 275-299
    • Scheffer, V.1
  • 21
    • 0041603815 scopus 로고    scopus 로고
    • Some estimates near the boundary for solutions to the non-stationary linearized Navier-Stokes equations
    • Seregin G.A. Some estimates near the boundary for solutions to the non-stationary linearized Navier-Stokes equations. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 271 (2000) 204-223
    • (2000) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) , vol.271 , pp. 204-223
    • Seregin, G.A.1
  • 22
    • 0041603848 scopus 로고    scopus 로고
    • Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary
    • Seregin G.A. Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary. J. Math. Fluid Mech. 4 1 (2002) 1-29
    • (2002) J. Math. Fluid Mech. , vol.4 , Issue.1 , pp. 1-29
    • Seregin, G.A.1
  • 23
    • 17444430349 scopus 로고    scopus 로고
    • 3, ∞-solutions to the Navier-Stokes equations up to boundary
    • 3, ∞-solutions to the Navier-Stokes equations up to boundary. Math. Ann. 332 1 (2005) 219-238
    • (2005) Math. Ann. , vol.332 , Issue.1 , pp. 219-238
    • Seregin, G.A.1
  • 24
    • 0036017441 scopus 로고    scopus 로고
    • Navier-Stokes equations with lower bounds on the pressure
    • Seregin G.A., and Šverák V. Navier-Stokes equations with lower bounds on the pressure. Arch. Ration. Mech. Anal. 163 1 (2002) 65-86
    • (2002) Arch. Ration. Mech. Anal. , vol.163 , Issue.1 , pp. 65-86
    • Seregin, G.A.1    Šverák, V.2
  • 25
    • 0000169262 scopus 로고
    • On the interior regularity of weak solutions of the Navier-Stokes equations
    • Serrin J. On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal. 9 (1962) 187-195
    • (1962) Arch. Ration. Mech. Anal. , vol.9 , pp. 187-195
    • Serrin, J.1
  • 26
    • 0001807443 scopus 로고
    • The initial value problem for the Navier-Stokes equations
    • Madison, WI, Univ. of Wisconsin Press, Madison, WI
    • Serrin J. The initial value problem for the Navier-Stokes equations. Nonlinear Problems, Proc. Sympos. Madison, WI (1963), Univ. of Wisconsin Press, Madison, WI 69-98
    • (1963) Nonlinear Problems, Proc. Sympos. , pp. 69-98
    • Serrin, J.1
  • 27
    • 0011944624 scopus 로고
    • Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes
    • Sohr H. Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes. Math. Z. 184 3 (1983) 359-375
    • (1983) Math. Z. , vol.184 , Issue.3 , pp. 359-375
    • Sohr, H.1
  • 28
    • 0345857776 scopus 로고    scopus 로고
    • A regularity class for the Navier-Stokes equations in Lorentz spaces
    • Sohr H. A regularity class for the Navier-Stokes equations in Lorentz spaces. J. Evol. Equ. 1 4 (2001) 441-467
    • (2001) J. Evol. Equ. , vol.1 , Issue.4 , pp. 441-467
    • Sohr, H.1
  • 29
    • 0011968533 scopus 로고
    • On the regularity of the pressure of weak solutions of Navier-Stokes equations
    • Sohr H., and Von Wahl W. On the regularity of the pressure of weak solutions of Navier-Stokes equations. Arch. Math. 46 5 (1986) 428-439
    • (1986) Arch. Math. , vol.46 , Issue.5 , pp. 428-439
    • Sohr, H.1    Von Wahl, W.2
  • 31
    • 84990553438 scopus 로고
    • On partial regularity results for the Navier-Stokes equations
    • Struwe M. On partial regularity results for the Navier-Stokes equations. Comm. Pure Appl. Math. 41 (1988) 437-458
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 437-458
    • Struwe, M.1
  • 32
    • 0000359176 scopus 로고    scopus 로고
    • Gradient estimation on Navier-Stokes equations
    • Tian G., and Xin Z. Gradient estimation on Navier-Stokes equations. Comm. Anal. Geom. 7 2 (1999) 221-257
    • (1999) Comm. Anal. Geom. , vol.7 , Issue.2 , pp. 221-257
    • Tian, G.1    Xin, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.