A mathematical theory is mounted for a complex system of equations derived by Gear and Grimshaw that models the strong interaction of two-dimensional, long, internal gravity waves propagating on neighboring pycnoclines in a stratified fluid. For the model in question, the Cauchy problem is of interest, and is shown to be globally well-posed in suitably strong function spaces. Our results make use of Kato's theory for abstract evolution equations together with somewhat delicate estimates obtained using techniques from harmonic analysis. In weak function classes, a local existence theory is developed. The system is shown to be susceptible to the dispersive blow-up phenomenon investigated recently by Bona and Saut for Korteweg-de Vries-type equations.
机构:
Sorbonne Univ, Lab Jacques Louis Lions, F-75005 Paris, FranceSorbonne Univ, Lab Jacques Louis Lions, F-75005 Paris, France
Barcena-Petisco, Jon Asier
Guerrero, Sergio
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Sorbonne Univ, Lab Jacques Louis Lions, F-75005 Paris, France
Univ Autonoma Madrid, Dept Matemat, Madrid 28049, Spain
Fdn Deusto, Chair Computat Math, Ave Univ 24, Bilbao 48007, Basque Country, SpainSorbonne Univ, Lab Jacques Louis Lions, F-75005 Paris, France
Guerrero, Sergio
Pazoto, Ademir F.
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机构:
Univ Fed Rio de Janeiro, Inst Matemat, CP 68530, BR-21941909 Rio De Janeiro, RJ, BrazilSorbonne Univ, Lab Jacques Louis Lions, F-75005 Paris, France
机构:
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou
Yunlong Lake Laboratory of Deep Underground Science and Engineering, Xuzhou
Research Center for Deep Ocean Science and Underwater Engineering, China University of Mining and Technology, XuzhouState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou
Tian Z.
Huang J.
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State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, XuzhouState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou
Huang J.
Song L.
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State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou
Research Center for Deep Ocean Science and Underwater Engineering, China University of Mining and Technology, XuzhouState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou
Song L.
Zhang M.
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机构:
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, XuzhouState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou
Zhang M.
Jia Y.
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机构:
Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Ocean University of China, QingdaoState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou
Jia Y.
Yue J.
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机构:
Research Center for Deep Ocean Science and Underwater Engineering, China University of Mining and Technology, Xuzhou
School of Resources and Geosciences, China University of Mining and Technology, XuzhouState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou
机构:
China Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
China Univ Min & Technol, Res Ctr Deep Ocean Sci & Underwater Engn, Xuzhou, Peoples R ChinaChina Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
Tian, Zhuangcai
Huang, Jinjian
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China Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R ChinaChina Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
Huang, Jinjian
Xiang, Jiaming
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China Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R ChinaChina Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
Xiang, Jiaming
Zhang, Shaotong
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机构:
Ocean Univ China, Frontiers Sci Ctr Deep Ocean Multispheres & Earth, Key Lab Submarine Geosci & Prospecting Tech, Coll Marine Geosci,MOE, Qingdao, Peoples R ChinaChina Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
Zhang, Shaotong
Wu, Jinran
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机构:
Australian Catholic Univ, Inst Learning Sci & Teacher Educ, Brisbane, Qld, AustraliaChina Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
Wu, Jinran
Liu, Xiaolei
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机构:
Ocean Univ China, Shandong Prov Key Lab Marine Environm & Geol Engn, Qingdao, Peoples R ChinaChina Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
Liu, Xiaolei
Luo, Tingting
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机构:
China Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
Natl Univ Singapore, Dept Chem & Biomol Engn, Singapore, SingaporeChina Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
Luo, Tingting
Yue, Jianhua
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机构:
China Univ Min & Technol, Res Ctr Deep Ocean Sci & Underwater Engn, Xuzhou, Peoples R China
China Univ Min & Technol, Sch Resources & Geosci, Xuzhou, Peoples R ChinaChina Univ Min & Technol, State Key Lab Intelligent Construct & Hlth Operat, Xuzhou 221116, Peoples R China
机构:
State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Research Center for Deep Ocean Science and Underwater Engineering, China University of Mining and TechnologyState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Zhuangcai Tian
Jinjian Huang
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机构:
State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and TechnologyState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Jinjian Huang
Jiaming Xiang
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机构:
State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and TechnologyState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Jiaming Xiang
Shaotong Zhang
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机构:
Frontiers Science Center for Deep Ocean Multispheres and Earth System, Key Lab of Submarine Geosciences and Prospecting Techniques, MOE, College of Marine Geosciences, Ocean University of ChinaState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Shaotong Zhang
Jinran Wu
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机构:
Institute for Learning Sciences & Teacher Education, Australian Catholic UniversityState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Jinran Wu
Xiaolei Liu
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机构:
Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Ocean University of ChinaState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Xiaolei Liu
Tingting Luo
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机构:
State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Department of Chemical and Biomolecular Engineering, National University of SingaporeState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology
Tingting Luo
Jianhua Yue
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机构:
Research Center for Deep Ocean Science and Underwater Engineering, China University of Mining and Technology
School of Resources and Geosciences, China University of Mining and TechnologyState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology