Sóng nước đứng do trọng lực và mao dẫn

Archive for Rational Mechanics and Analysis - Tập 217 - Trang 741-830 - 2015
Thomas Alazard1, Pietro Baldi2
1Département de Mathématiques et Applications, Ecole Normale Supérieure, Paris, France
2Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Naples, Italy

Tóm tắt

Bài báo đề cập đến các phương trình sóng nước 2D do trọng lực và mao dẫn trong biểu thức Hamilton, giải quyết vấn đề tương tác phi tuyến giữa sóng phẳng và phản xạ của nó khi gặp tường thẳng đứng. Kết quả chính là việc xây dựng các nghiệm đứng (cụ thể là tuần hoàn theo thời gian và không gian, và không di chuyển) với biên độ nhỏ, đạt độ đều Sobolev, cho hầu hết các giá trị của hệ số căng bề mặt và cho một tập hợp lớn các tần số thời gian. Đây là một kết quả tồn tại cho một hệ thống của các phương trình vi phân riêng phần giả tự trị gần như tuyến tính, Hamilton và có thể đảo ngược với các số chia nhỏ. Chứng minh là sự kết hợp của nhiều kỹ thuật khác nhau, như sơ đồ Nash–Moser, phân tích vi mô và phân tích phân nhánh.

Từ khóa

#sóng nước #phương trình Hamilton #tương tác phi tuyến #độ đều Sobolev #phương trình vi phân riêng phần #phân nhánh

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