Phân tích nhóm Lie, nghiệm chính xác và định luật bảo toàn cho phương trình Navier–Stokes đẳng nhiệt nén được

Engineering with Computers - Tập 38 - Trang 2027-2036 - 2020
Ram Jiwari1, Vikas Kumar2, Sukhveer Singh1
1Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India
2Department of Mathematics, D.A.V. College Pundri, Kaithal, India

Tóm tắt

Nghiên cứu hiện tại dành cho các phương trình Navier–Stokes đẳng nhiệt nén một chiều với luật áp suất tổng quát. Phương pháp Nhóm Lie được sử dụng để chuyển các phương trình Navier–Stokes đẳng nhiệt nén thành một hệ các phương trình vi phân thường phi tuyến cao có các biến đổi tương đồng phù hợp. Do đó, với sự trợ giúp của các nghiệm chính xác của các phương trình vi phân thường đã được giảm bớt, biến tương đồng và nghiệm tương đồng, các nghiệm chính xác của phương trình chính được thu được. Cuối cùng, bằng cách sử dụng hệ số bảo toàn, chúng tôi tìm thấy tập hợp hoàn chỉnh các định luật bảo toàn địa phương của các phương trình Navier–Stokes đẳng nhiệt nén cho các hệ số hằng số tùy ý.

Từ khóa

#Navier–Stokes #đẳng nhiệt #bảo toàn #phương trình vi phân thường #nhóm Lie

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