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Tiêu chuẩn tính điều hòa dựa trên dao động áp suất cho phương trình Navier-Stokes 3D
Tóm tắt
Chúng tôi đưa ra một tiêu chuẩn tính điều hòa mới dựa trên dao động của đạo hàm theo thời gian của áp suất cho phương trình Navier-Stokes 3D trong một miền $$\mathcal {D}\subset {\mathbb {R}}^3$$. Quan sát chính trong quá trình chứng minh là áp suất đầu ra được định nghĩa bởi $${\overline{Q}} (x,t)= \frac{1}{2} |v(x,t)|^2 + {\bar{p}}(x,t), $$ trong đó $${\bar{p}} (x,t)= p(x,t)-\int \limits ^t_{t_0} \sup _{ y\in \Omega } (\partial _s p(y,s) -|\omega (y,s)|^2)\textrm{d}s $$ với p(x, t) là áp suất và $$\omega $$ là độ xoáy thỏa mãn nguyên lý cực đại parabol trong $$ \Omega \times ( t_0, T)$$ với $$\Omega \Subset \mathcal {D}$$.
Từ khóa
Tài liệu tham khảo
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