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Các Phương Trình Boussinesq Ba Chiều với Tính Quy Hoạch Trong Một Đạo Hàm Hướng Dẫn của Áp Suất
Tóm tắt
Công trình này thiết lập một tiêu chí cải tiến về độ đều mới theo dạng logarithmic cho các phương trình Boussinesq ba chiều dựa trên một đạo hàm theo hướng của áp suất (tức là, $$\partial _{3}P$$) trong không gian Lebesgue dị hướng. Cụ thể hơn, chúng tôi đã chứng minh rằng nếu $$\begin{aligned}&\displaystyle \int _{0}^{T}\frac{\left\| \Vert \partial _{3}P(\cdot ,t)\Vert _{L^{\gamma }_{x_{3}}} \right\| _{L^{\alpha }_{x_{1}x_{2}}}^{\beta }}{1+\ln (1+\Vert \theta (\cdot ,t)\Vert _{L^{4}})}\text {d}t<\infty ,\\&\text {nơi } \frac{2}{\beta }+\frac{1}{\gamma }+\frac{2}{\alpha }=k\in [2,3) \text { và }\frac{3}{k}\le \gamma \le \alpha < \frac{1}{k-2}, \end{aligned}$$ cho một số $$T>0$$, thì nghiệm tương ứng $$(u,\theta )$$ cho các phương trình Boussinesq ba chiều là đều trên [0, T].
Từ khóa
#phương trình Boussinesq #độ đều #đạo hàm hướng #không gian Lebesgue #áp suấtTài liệu tham khảo
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