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Bảo Tồn Năng Lượng của Các Giải Phương Trình DiPerna–Lions đối với Hệ Vlasov–Maxwell
Journal of Nonlinear Science - 2023
Tóm tắt
Trong bài báo này, chúng tôi đưa ra các điều kiện đủ để bảo tồn năng lượng của các giải pháp DiPerna–Lions được đưa ra trong DiPerna và Lions (Commun Pure Appl Math 42:729–757, 1989), Rein (Commun Math Sci 2:145–158, 2004) cho các hệ Vlasov–Maxwell trong $$\mathbb {R}^3$$, chỉ yêu cầu mật độ vĩ mô $$\rho \in L^2_tL^2_\textrm{loc}$$ đối với trường hợp tương đối và $$\vert \xi \vert f\in L^2_{t,x}L^1_{\xi }$$ cho trường hợp không tương đối, cải thiện các kết quả trong Sospedra–Alfonso (Commun Math Sci 8:901–908, 2010), Bardos và cộng sự (Q Appl Math 78:193–217, 2020). Tiếp theo, bằng cách làm mềm theo thời gian hai lần với các tham số khác nhau và các biểu thức yếu liên quan đến $$t=0$$, chúng tôi đạt được các kết quả tương tự cho các giải pháp được đưa ra trong Guo (Commun Math Phys 154:245–263, 1993) với tính chất đều trong thời gian thấp cho các hệ Vlasov–Maxwell trong các miền giới hạn dưới một số điều kiện lớp biên.
Từ khóa
#DiPerna-Lions #Vlasov-Maxwell #bảo tồn năng lượng #giải pháp #mật độ vĩ mô #làm mềm theo thời gianTài liệu tham khảo
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