Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Giải pháp mạnh toàn cục cho chất lỏng từ tính thủy động lực học không đồng nhất hai chiều với độ nhớt phụ thuộc vào mật độ và vùng chân không
Tóm tắt
Trong bài viết này, chúng tôi nghiên cứu một bài toán giá trị biên ban đầu cho hệ thống MHD hai chiều không đồng nhất không nén với độ nhớt phụ thuộc vào mật độ. Đầu tiên, chúng tôi thiết lập một tiêu chí nổ (blow-up criterion) cho các nghiệm mạnh có chân không. Cụ thể, nghiệm mạnh tồn tại toàn cục nếu $\|\nabla \mu (\rho )\|_{L^{\infty }(0, T; L^{p})}$ là hữu hạn. Thứ hai, chúng tôi chứng minh rằng nghiệm mạnh tồn tại toàn cục (theo thời gian) chỉ khi $\|\nabla \mu (\rho _{0})\|_{L^{p}}$ là đủ nhỏ, ngay cả khi có sự hiện diện của chân không.
Từ khóa
#MHD #chất lỏng không nén #độ nhớt phụ thuộc vào mật độ #nghiệm mạnh #chân khôngTài liệu tham khảo
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