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Groups of asymptotic diffeomorphisms
1. | Northeastern University, Boston, MA 02115, United States, United States |
References:
[1] |
V. Arnold, Sur la geometrié differentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluids parfaits, Ann. Inst. Fourier, 16 (1966), 319-361.
doi: 10.5802/aif.233. |
[2] |
R. Bartnik, The mass of an asymptotically flat manifold, Comm. Pure Appl. Math, 39 (1986), 661-693.
doi: 10.1002/cpa.3160390505. |
[3] |
I. Bondareva and M. Shubin, Uniqueness of the solution of the Cauchy problem for the Korteweg - de Vries equation in classes of increasing functions, Moscow Univ. Math. Bulletin, 40 (1985), 53-57. |
[4] |
I. Bondareva and M. Shubin, Equations of Korteweg-de Vries type in classes of increasing functions, J. Soviet Math., 51 (1990), 2323-2332.
doi: 10.1007/BF01094991. |
[5] |
J. P. Bourguignon and H. Brezis, Remarks on the Euler equation, J. Func. Anal., 15 (1974), 341-363. |
[6] |
R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett., 71 (1993), 1661-1664.
doi: 10.1103/PhysRevLett.71.1661. |
[7] |
M. Cantor, Perfect fluid flows over $\mathbb{R}^{N}$ with asymptotic conditions, J. Func. Anal., 18 (1975), 73-84.
doi: 10.1016/0022-1236(75)90030-0. |
[8] |
A. Constantin, Existence of permanent and breaking waves for a shallow water equation: A geometric approach, Ann. Inst. Four. Grenoble, 50 (2000), 321-362.
doi: 10.5802/aif.1757. |
[9] |
D. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math., 92 (1970), 102-163.
doi: 10.2307/1970699. |
[10] |
H. Inci, T. Kappeler and P. Topalov, On the regularity of the composition of diffeomorphisms, Mem. Amer. Math. Soc., 226 (2013), no. 1062.
doi: 10.1090/S0065-9266-2013-00676-4. |
[11] |
T. Kappeler, P. Perry, M. Shubin and P. Topalov, Solutions of mKdV in classes of functions unbounded at infinity, J. Geom. Anal., 18 (2008), 443-477.
doi: 10.1007/s12220-008-9013-3. |
[12] |
C. Kenig, G. Ponce and L. Vega, Global solutions for the KdV equation with unbounded data, J. Diff. Equations, 139 (1997), 339-364.
doi: 10.1006/jdeq.1997.3297. |
[13] |
R. McOwen, The behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math., 32 (1979), 783-795.
doi: 10.1002/cpa.3160320604. |
[14] |
R. McOwen, Partial Differential Equations: Methods and Applications, 2nd ed, Pearson, 2003. |
[15] |
R. McOwen and P. Topalov, Asymptotics in shallow water waves, Discrete Contin. Dyn. Syst., 35 (2015), 3103-3131.
doi: 10.3934/dcds.2015.35.3103. |
[16] |
R. McOwen and P. Topalov, Spatial asymptotic expansions in the incompressible Euler equation, arXiv:1606.08059. |
[17] |
A. Menikoff, The existence of unbounded solutions of the Korteweg-de Vries equation, Comm. Pure Appl. Math., 25 (1972), 407-432.
doi: 10.1002/cpa.3160250404. |
[18] |
P. Michor and D. Mumford, A zoo of diffeomorphisms groups on $\mathbb{R}^{N}$, Ann. Glob. Anal. Geom., 44, 529-540.
doi: 10.1007/s10455-013-9380-2. |
[19] |
G. Misiolek, A shallow water equation as a geodesic flow on the Bott-Visaro group, J. Geom. Phys., 24 (1998), 203-208.
doi: 10.1016/S0393-0440(97)00010-7. |
[20] |
D. Montgomery, On continuity in topological groups, Bull. Amer. Math. Soc., 42 (1936), 879-882.
doi: 10.1090/S0002-9904-1936-06456-6. |
show all references
References:
[1] |
V. Arnold, Sur la geometrié differentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluids parfaits, Ann. Inst. Fourier, 16 (1966), 319-361.
doi: 10.5802/aif.233. |
[2] |
R. Bartnik, The mass of an asymptotically flat manifold, Comm. Pure Appl. Math, 39 (1986), 661-693.
doi: 10.1002/cpa.3160390505. |
[3] |
I. Bondareva and M. Shubin, Uniqueness of the solution of the Cauchy problem for the Korteweg - de Vries equation in classes of increasing functions, Moscow Univ. Math. Bulletin, 40 (1985), 53-57. |
[4] |
I. Bondareva and M. Shubin, Equations of Korteweg-de Vries type in classes of increasing functions, J. Soviet Math., 51 (1990), 2323-2332.
doi: 10.1007/BF01094991. |
[5] |
J. P. Bourguignon and H. Brezis, Remarks on the Euler equation, J. Func. Anal., 15 (1974), 341-363. |
[6] |
R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett., 71 (1993), 1661-1664.
doi: 10.1103/PhysRevLett.71.1661. |
[7] |
M. Cantor, Perfect fluid flows over $\mathbb{R}^{N}$ with asymptotic conditions, J. Func. Anal., 18 (1975), 73-84.
doi: 10.1016/0022-1236(75)90030-0. |
[8] |
A. Constantin, Existence of permanent and breaking waves for a shallow water equation: A geometric approach, Ann. Inst. Four. Grenoble, 50 (2000), 321-362.
doi: 10.5802/aif.1757. |
[9] |
D. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math., 92 (1970), 102-163.
doi: 10.2307/1970699. |
[10] |
H. Inci, T. Kappeler and P. Topalov, On the regularity of the composition of diffeomorphisms, Mem. Amer. Math. Soc., 226 (2013), no. 1062.
doi: 10.1090/S0065-9266-2013-00676-4. |
[11] |
T. Kappeler, P. Perry, M. Shubin and P. Topalov, Solutions of mKdV in classes of functions unbounded at infinity, J. Geom. Anal., 18 (2008), 443-477.
doi: 10.1007/s12220-008-9013-3. |
[12] |
C. Kenig, G. Ponce and L. Vega, Global solutions for the KdV equation with unbounded data, J. Diff. Equations, 139 (1997), 339-364.
doi: 10.1006/jdeq.1997.3297. |
[13] |
R. McOwen, The behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math., 32 (1979), 783-795.
doi: 10.1002/cpa.3160320604. |
[14] |
R. McOwen, Partial Differential Equations: Methods and Applications, 2nd ed, Pearson, 2003. |
[15] |
R. McOwen and P. Topalov, Asymptotics in shallow water waves, Discrete Contin. Dyn. Syst., 35 (2015), 3103-3131.
doi: 10.3934/dcds.2015.35.3103. |
[16] |
R. McOwen and P. Topalov, Spatial asymptotic expansions in the incompressible Euler equation, arXiv:1606.08059. |
[17] |
A. Menikoff, The existence of unbounded solutions of the Korteweg-de Vries equation, Comm. Pure Appl. Math., 25 (1972), 407-432.
doi: 10.1002/cpa.3160250404. |
[18] |
P. Michor and D. Mumford, A zoo of diffeomorphisms groups on $\mathbb{R}^{N}$, Ann. Glob. Anal. Geom., 44, 529-540.
doi: 10.1007/s10455-013-9380-2. |
[19] |
G. Misiolek, A shallow water equation as a geodesic flow on the Bott-Visaro group, J. Geom. Phys., 24 (1998), 203-208.
doi: 10.1016/S0393-0440(97)00010-7. |
[20] |
D. Montgomery, On continuity in topological groups, Bull. Amer. Math. Soc., 42 (1936), 879-882.
doi: 10.1090/S0002-9904-1936-06456-6. |
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