Boussinesq方程组在Besov空间中局部解的存在性和延拓准则

doi:10.12386/A2010sxxb0051

鏁板瀛︽姤鈥衡�� 2010, Vol. 53 鈥衡�� Issue (3): 455-468.DOI: 10.12386/A2010sxxb0051

鈥� 璁烘枃鈥� 涓婁竴绡� 涓嬩竴绡�

Boussinesq鏂圭▼缁勫湪Besov绌洪棿涓眬閮ㄨВ鐨勫瓨鍦ㄦ�у拰寤舵嫇鍑嗗垯

鍘熶繚鍏�

娌冲崡鐞嗗伐澶у鏁板涓庝俊鎭瀛﹀闄� 鐒︿綔 454000

鏀剁鏃ユ湡:2008-03-25 淇洖鏃ユ湡:2009-10-27 鍑虹増鏃ユ湡:2010-05-15 鍙戝竷鏃ユ湡:2010-05-30
閫氳浣滆��: 鍘熶繚鍏�
鍩洪噾璧勫姪:
鍥藉鑷劧绉戝鍩洪噾璧勫姪椤圭洰 (10771052);娌冲崡鐪佸垱鏂板瀷绉戞妧浜烘墠闃熶紞寤鸿宸ョ▼;娌冲崡鐪侀珮鏍＄鎶�鍒涙柊浜烘墠鏀寔璁″垝 (2009HASTIT007)鍙婃渤鍗楃悊宸ュぇ瀛﹀崥澹熀閲� (B2008-62)

Local Existence and Continuity Conditions of Solutions to the Boussinesq Equations in Besov Spaces

Bao Quan YUAN

School of Mathematics and Informatics, He'nan Polytechnic University, He'nan Province, Jiaozuo 454000, P. R. China

Received:2008-03-25 Revised:2009-10-27 Online:2010-05-15 Published:2010-05-30

鎽樿/Abstract

鎽樿锛� 鏈枃鐮旂┒浜岀淮鏃犵矘鎬oussinesq鏂圭▼缁勫湪瓒呬复鐣孊esov绌洪棿,s>1+2/p, 1<p<+∞, 1≤q≤+∞鍜屼复鐣孊esov绌洪棿, p∈(1,+∞)灞�閮ㄨВ鐨勫瓨鍦ㄦ�у拰鍞竴鎬�, 骞朵笖寰楀埌浜嗗眬閮ㄨВ浠呬娇鐢�∇θ鐨勭垎鐮村噯鍒�, 璇ュ噯鍒欏皢Beale--Kato--Majda鍨嬪噯鍒欐帹骞垮埌浜嗛綈娆esov绌洪棿.

鍏抽敭璇�: Boussinesq鏂圭▼缁�, Besov绌洪棿, 瀛樺湪鎬т笌鍞竴鎬�, 鐖嗙牬鍑嗗垯

Abstract: In this paper, we study the 2D invisid Boussinesq equations, and prove the local existence and uniqueness of solutions in Besov space for super critical case s > 1 + 2/p, 1 < p < +∞, 1≤q≤+∞, and critical case s = 1 + 2/p with p∈(1,+∞) and q = 1. The blow-up criteria of the local solutions constructed are also obtained, which improves the Beale--Kato--Majda type criterion in homogeneous Besov space . Moreover, our blow-up criteria are only imposed on ∇θ.

Key words: Boussinesq equations, Besov spaces, existence and uniqueness, blow-up criteria

涓浘鍒嗙被鍙�:

O175.2

鍘熶繚鍏�. Boussinesq鏂圭▼缁勫湪Besov绌洪棿涓眬閮ㄨВ鐨勫瓨鍦ㄦ�у拰寤舵嫇鍑嗗垯[J]. 鏁板瀛︽姤, 2010, 53(3): 455-468.

Bao Quan YUAN. Local Existence and Continuity Conditions of Solutions to the Boussinesq Equations in Besov Spaces[J]. Acta Mathematica Sinica, Chinese Series, 2010, 53(3): 455-468.

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閾炬帴鏈枃: https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/10.12386/A2010sxxb0051

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Boussinesq鏂圭▼缁勫湪Besov绌洪棿涓眬閮ㄨВ鐨勫瓨鍦ㄦ�у拰寤舵嫇鍑嗗垯

Local Existence and Continuity Conditions of Solutions to the Boussinesq Equations in Besov Spaces

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