Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Sự bùng nổ trong thời gian hữu hạn của các nghiệm cổ điển đối với hệ thống nước nông quay với độ nhớt suy giảm
Tóm tắt
Trong bài báo này, chúng tôi nghiên cứu hệ thống nước nông quay với dữ liệu ban đầu chứa không khí, độ nhớt của hệ thống là suy giảm, và lực Coriolis, lực mao dẫn và lực cản turbulent từ ma sát được xem xét. Khi một khối lượng dương nằm trong vùng chân không giới hạn (nhóm khối lượng tách biệt), ban đầu, chúng tôi chứng minh rằng bất kỳ nghiệm cổ điển nào cho bài toán giá trị biên ban đầu và bài toán tuần hoàn sẽ bùng nổ trong thời gian hữu hạn. Điều này cho thấy rằng các nghiệm yếu toàn cục đạt được trong Bresch và Desjardins (Commun Math Phys 238(1–2):211–223, 2003) không thể là nghiệm cổ điển miễn là dữ liệu ban đầu thừa nhận một nhóm khối lượng tách biệt. Nó cũng cho thấy rằng so với các thuộc tính làm mịn do các thành phần mao dẫn và lực cản cung cấp, sự suy giảm của độ nhớt đóng vai trò nổi bật trong bài toán quy tắc toàn cục và dẫn đến sự kỳ dị trong thời gian hữu hạn của các nghiệm mịn.
Từ khóa
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