论文标题
Navier-Stokes类型方程与De Rham复合物相关的弱解的存在定理
Existence theorem of a weak solution for Navier-Stokes type equations associated with de Rham complex
论文作者
论文摘要
令$ \ {d_q，λ^{q} \} $在平滑的紧凑型封闭的歧管上$ x $上的$ \ mathbb {r}^3 $，带有laplacians $Δ__{q} $。我们考虑与抛物线差分运算符$ \ partial_t +δ_2 + n^{2} $相关联的操作员方程式在复杂的第二步与零订单$ n^{2} $的非线性bi-differential Operation的第二步。在复杂的下一步中使用投影，我们表明该方程在特殊的Bochner-Sobolev类型功能空间中具有独特的解决方案，以适用于某些时间（足够小）$ t^* $。
Let $ \{d_q, Λ^{q} \} $ be de Rham complex on a smooth compact closed manifold $X$ over $ \mathbb{R}^3 $ with Laplacians $Δ_{q} $. We consider operator equations, associated with the parabolic differential operators $\partial_t + Δ_2 + N^{2} $ on the second step of complex with nonlinear bi-differential operator of zero order $ N^{2} $. Using by projection on the next step of complex we show that the equation has unique solution in special Bochner-Sobolev type functional spaces for some (small enough) time $ T^* $.
