带阻尼项不可压Euler方程爆破解的存在性

The Existence of Damping Incompressible Euler Equation Explosive Solutions

研究了带阻尼项α||u||L∞u(α>0)的不可压Euler方程。首先,我们利用Galerkin方法、Poincare不等式、Sobolev嵌入定理、能量不等式,我们得到了带有阻尼项不可压Euler方程有类似于古典不可压Euler方程的不变性(爆破解的存在性)。其次,我们证明了古典不可压Euler方程的解v(x,t)和带有非线性项不可压Euler方程解u(x,t)之间存在下面关系:u(x,t)=φ(t,x)v(x,t)φ(t)=λ∫t0exp[∫τ0||u||L∞ds]dτ)。

This thesis studies the damping α｜｜u｜｜L-u（α〉0） incompressible Euler equation. Firstly, we proved the existence of classic incompressible Euler Equation explosive solution by using Galerkin method, Poincare inequality, Sobolev embedding theorem, and energy inequality. Besides, we found the interrelationship between the solution of classic incompressible Euler Equation v（x,t） and the solution of nonlinear incompressible Euler equation u（x,t）=φ（t,x）v（x,t）φ（t）=λ∫t0exp[∫τ0｜｜u｜｜L-ds]dτ）.