Về các điểm nổ tự tương tự trong thời gian hữu hạn của mô hình De Gregorio trên dòng thực

Springer Science and Business Media LLC - Tập 402 Số 3 - Trang 2791-2829 - 2023
Huang, De1, Tong, Jiajun2, Wei, Dongyi1
1School of Mathematical Sciences, Peking University, Beijing, China
2Beijing International Center for Mathematical Research, Peking University, Beijing, China

Tóm tắt

Chúng tôi chỉ ra rằng mô hình De Gregorio trên dòng thực có vô số nghiệm tự tương tự được hỗ trợ compact, phân biệt dưới sự phân tỉ lệ và sẽ phát nổ trong thời gian hữu hạn. Những nghiệm tự tương tự này thuộc về hai lớp: lớp cơ bản và lớp tổng quát. Lớp cơ bản bao gồm các nghiệm vô hạn đếm được, là các hàm riêng của một toán tử compact tự liên hợp. Cụ thể, hàm riêng hàng đầu trùng với nghiệm điểm kỳ hữu hạn của mô hình De Gregorio vừa được thu được thông qua các phương pháp số. Lớp tổng quát bao gồm các nghiệm phức tạp hơn có thể được tìm thấy bằng cách giải các bài toán giá trị riêng phi tuyến liên quan đến cùng một toán tử compact.

Từ khóa

#mô hình De Gregorio #điểm nổ tự tương tự #nghiệm tự tương tự #toán tử compact #hàm riêng #thời gian hữu hạn

Tài liệu tham khảo

citation_journal_title=Entropy Quantum; citation_title=Trace inequalities and quantum entropy: an introductory course; citation_author=E Carlen; citation_volume=529; citation_publication_date=2010; citation_pages=73-140; citation_doi=10.1090/conm/529/10428; citation_id=CR1 citation_journal_title=Adv. Math.; citation_title=Infinite energy solutions of the surface quasi-geostrophic equation; citation_author=A Castro, D Córdoba; citation_volume=225; citation_issue=4; citation_publication_date=2010; citation_pages=1820-1829; citation_doi=10.1016/j.aim.2010.04.018; citation_id=CR2 citation_journal_title=Ann. Math.; citation_title=Formation of singularities for a transport equation with nonlocal velocity; citation_author=A Córdoba, D Córdoba, MA Fontelos; citation_volume=162; citation_publication_date=2005; citation_pages=1377-1389; citation_doi=10.4007/annals.2005.162.1377; citation_id=CR3 Chen, J.: On the regularity of the De Gregorio model for the 3D Euler equations. J. Eur. Math. Soc (to appear). Preprint arXiv:2107.04777 citation_journal_title=Nonlinearity; citation_title=Singularity formation and global well-posedness for the generalized Constantin-Lax-Majda equation with dissipation; citation_author=J Chen; citation_volume=33; citation_issue=5; citation_publication_date=2020; citation_pages=2502; citation_doi=10.1088/1361-6544/ab74b0; citation_id=CR5 citation_journal_title=Arch. Ration. Mech. Anal.; citation_title=On the slightly perturbed De Gregorio model on ; citation_author=J Chen; citation_volume=241; citation_issue=3; citation_publication_date=2021; citation_pages=1843-1869; citation_doi=10.1007/s00205-021-01685-w; citation_id=CR6 Chen, J., Hou, T.Y., Huang, D.: Matlab codes for computer-aided proofs in the paper “on the finite time blowup of the De Gregorio model for the 3D Euler equations”. https://www.dropbox.com/sh/jw3hkkgx9q6m9fj/AAC46ea4QorTCNAzVTkMQQnOa?dl=0 citation_journal_title=Commun. Pure Appl. Math.; citation_title=On the finite time blowup of the De Gregorio model for the 3D Euler equations; citation_author=J Chen, TY Hou, D Huang; citation_volume=74; citation_issue=6; citation_publication_date=2021; citation_pages=1282-1350; citation_doi=10.1002/cpa.21991; citation_id=CR8 citation_journal_title=Commun. Pure Appl. Math.; citation_title=A simple one-dimensional model for the three-dimensional vorticity equation; citation_author=P Constantin, PD Lax, A Majda; citation_volume=38; citation_issue=6; citation_publication_date=1985; citation_pages=715-724; citation_doi=10.1002/cpa.3160380605; citation_id=CR9 citation_journal_title=J. Stat. Phys.; citation_title=On a one-dimensional model for the three-dimensional vorticity equation; citation_author=S Gregorio; citation_volume=59; citation_issue=5; citation_publication_date=1990; citation_pages=1251-1263; citation_doi=10.1007/BF01334750; citation_id=CR10 citation_journal_title=Math. Methods Appl. Sci.; citation_title=A partial differential equation arising in a 1D model for the 3D vorticity equation; citation_author=S Gregorio; citation_volume=19; citation_issue=15; citation_publication_date=1996; citation_pages=1233-1255; citation_doi=10.1002/(SICI)1099-1476(199610)19:15<1233::AID-MMA828>3.0.CO;2-W; citation_id=CR11 citation_journal_title=J. Funct. Anal.; citation_title=Well-posedness for a transport equation with nonlocal velocity; citation_author=H Dong; citation_volume=255; citation_issue=11; citation_publication_date=2008; citation_pages=3070-3097; citation_doi=10.1016/j.jfa.2008.08.005; citation_id=CR12 citation_journal_title=Arch. Ration. Mech. Anal.; citation_title=On the effects of advection and vortex stretching; citation_author=TM Elgindi, I-J Jeong; citation_volume=235; citation_issue=3; citation_publication_date=2020; citation_pages=1763-1817; citation_doi=10.1007/s00205-019-01455-9; citation_id=CR13 citation_journal_title=J. Nonlinear Sci.; citation_title=Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations; citation_author=TY Hou, R Li; citation_volume=16; citation_issue=6; citation_publication_date=2006; citation_pages=639-664; citation_doi=10.1007/s00332-006-0800-3; citation_id=CR14 citation_journal_title=Commun. Pure Appl. Math. A J. Issued Courant Inst. Math. Sci.; citation_title=Dynamic stability of the three-dimensional axisymmetric Navier–Stokes equations with swirl; citation_author=TY Hou, C Li; citation_volume=61; citation_issue=5; citation_publication_date=2008; citation_pages=661-697; citation_doi=10.1002/cpa.20212; citation_id=CR15 citation_journal_title=Arch. Ration. Mech. Anal.; citation_title=On the De Gregorio modification of the Constantin-Lax-Majda model; citation_author=H Jia, S Stewart, V Sverak; citation_volume=231; citation_issue=2; citation_publication_date=2019; citation_pages=1269-1304; citation_doi=10.1007/s00205-018-1298-1; citation_id=CR16 citation_journal_title=Math. Model. Nat. Phenomena; citation_title=Regularity and blow up for active scalars; citation_author=A Kiselev; citation_volume=5; citation_issue=4; citation_publication_date=2010; citation_pages=225-255; citation_doi=10.1051/mmnp/20105410; citation_id=CR17 citation_journal_title=Commun. Pure Appl. Math. A J. Issued by the Courant Inst. Math. Sci.; citation_title=On the stabilizing effect of convection in three-dimensional incompressible flows; citation_author=Z Lei, TY Hou; citation_volume=62; citation_issue=4; citation_publication_date=2009; citation_pages=501-564; citation_id=CR18 citation_journal_title=Commun. Math. Phys.; citation_title=On the Constantin-Lax-Majda model with convection; citation_author=Z Lei, J Liu, X Ren; citation_volume=375; citation_issue=1; citation_publication_date=2020; citation_pages=765-783; citation_doi=10.1007/s00220-019-03584-4; citation_id=CR19 citation_journal_title=Phys. Rev. A; citation_title=Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension; citation_author=MJ Landman, GC Papanicolaou, C Sulem, P-L Sulem; citation_volume=38; citation_issue=8; citation_publication_date=1988; citation_pages=3837; citation_doi=10.1103/PhysRevA.38.3837; citation_id=CR20 citation_journal_title=Adv. Math.; citation_title=Blow-up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation; citation_author=D Li, J Rodrigo; citation_volume=217; citation_issue=6; citation_publication_date=2008; citation_pages=2563-2568; citation_doi=10.1016/j.aim.2007.11.002; citation_id=CR21 citation_journal_title=J. Nonlinear Sci.; citation_title=Collapse versus blow-up and global existence in the generalized Constantin-Lax-Majda equation; citation_author=PM Lushnikov, DA Silantyev, M Siegel; citation_volume=31; citation_issue=5; citation_publication_date=2021; citation_pages=1-56; citation_doi=10.1007/s00332-021-09737-x; citation_id=CR22 Martınez, A.C.: Nonlinear and nonlocal models in fluid mechanics (2010) citation_journal_title=Phys. Rev. A; citation_title=Focusing singularity of the cubic Schrödinger equation; citation_author=DW McLaughlin, GC Papanicolaou, C Sulem, P-L Sulem; citation_volume=34; citation_issue=2; citation_publication_date=1986; citation_pages=1200; citation_doi=10.1103/PhysRevA.34.1200; citation_id=CR24 citation_journal_title=J. Phys. Soc. Jpn.; citation_title=On the role of the convection term in the equations of motion of incompressible fluid; citation_author=H Okamoto, K Ohkitani; citation_volume=74; citation_issue=10; citation_publication_date=2005; citation_pages=2737-2742; citation_doi=10.1143/JPSJ.74.2737; citation_id=CR25 citation_journal_title=Nonlinearity; citation_title=On a generalization of the Constantin-Lax-Majda equation; citation_author=H Okamoto, T Sakajo, M Wunsch; citation_volume=21; citation_issue=10; citation_publication_date=2008; citation_pages=2447; citation_doi=10.1088/0951-7715/21/10/013; citation_id=CR26 citation_journal_title=Commun. Pure Appl. Math.; citation_title=Explicit solutions of the viscous model vorticity equation; citation_author=S Schochet; citation_volume=39; citation_issue=4; citation_publication_date=1986; citation_pages=531-537; citation_doi=10.1002/cpa.3160390404; citation_id=CR27 citation_journal_title=Trans. Am. Math. Soc.; citation_title=On a transport equation with nonlocal drift; citation_author=L Silvestre, V Vicol; citation_volume=368; citation_issue=9; citation_publication_date=2016; citation_pages=6159-6188; citation_doi=10.1090/tran6651; citation_id=CR28 Sverak, V.: A video lecture on “Small scale dynamics in fluid motion”. https://scgp.stonybrook.edu/video_portal/video.php?id=5281 citation_journal_title=Commun. Math. Sci.; citation_title=The generalized Constantin-Lax-Majda equation revisited; citation_author=M Wunsch; citation_volume=9; citation_issue=3; citation_publication_date=2011; citation_pages=929-936; citation_doi=10.4310/CMS.2011.v9.n3.a12; citation_id=CR30