N维不可压无阻尼Oldroyd-B模型的最优衰减  

Optimal Decay for the N-Dimensional Incompressible Oldroyd-B Model Without Damping Mechanism

作　　者：谢倩倩 翟小平 董柏青 Xie Qianqian;Zhai Xiaoping;Dong Boqing(Department of Mathematics and Statistics,Hefei University,Hefei 230601;School of Mathematics and Statistics,Shenzhen University,Shenzhen 518060;School of Mathematical Science,Anhui University,Hefei 230601)

机构地区：[1]合肥学院中德应用数学研究所&数学与统计系,合肥230601 [2]深圳大学数学与统计学院,深圳518060 [3]安徽大学数学科学学院,合肥230601

出　　处：《数学物理学报（A辑）》2021年第3期762-769,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11601533,11871346);广东省自然科学基金(2018A030313024);深圳市自然科学基金(JCYJ20180305125554234);深圳大学科研基金(2017056)。

摘　　要：对于n(n≥2)维不可压无阻尼Oldroyd-B模型,运用能量方法以及Besov空间中高低频分解技术,该文得到了关于强解的最优衰减速率.具体来说,充分利用方程的特殊结构,交换子估计以及Besov空间之间的各种插值定理,对于任意的初值(u0,τ0)∈B˙_(2,1)^(−s)(Rn),该文得到了关于强解(参见文献[18])的最优衰减速率||Λ^(α)(u,Λ^(−1)Pdivτ)||_(Lq)≤C(1+t)^(−n/4−(α+s)q−n/2q),Λ^(=def)√−Δ,其中指标满足1−n/2<s<n/p,2≤p≤min(4,2n/(n−2))(n=2时,p≠4),p≤q≤∞,n/q−n/p−s<α≤n/q−1.该文的方法也使用于其它抛物-双曲耦合的系统.By a new energy approach involved in the high frequency and low frequency decomposition in the Besov spaces,we obtain the optimal decay for the incompressible Oldroyd-B model without damping mechanism in Rn(n≥2).More precisely,let(u,τ)be the global small solutions constructed in[18],we prove for any(u0,τ0)∈B˙_(2,1)^(−s)(Rn)that||Λ^(α)(u,Λ^(−1)Pdivτ)||_(Lq)≤C(1+t)^(−n/4−(α+s)q−n/2q),Λ^(=def)√−Δ,with 1−n/2<s<n/p,2≤p≤min(4,2n/(n−2)),p≠4 if n=2,and p≤q≤∞,n/q−n/p−s<α≤n/q−1.The proof relies heavily on the special dissipative structure of the equations and some commutator estimates and various interpolations between Besov type spaces.The method also works for other parabolic-hyperbolic systems in which the Fourier splitting technique is invalid.

关 键 词：Oldroyd-B模型 时间衰减估计 BESOV空间 

分 类 号：O37[理学—流体力学]