Biharmonic wave maps: Local wellposedness in high regularity

Herr S, Lamm T, Schmid T, Schnaubelt R (2020)
Nonlinearity 33(5): 2270-2305.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Autor*in
Herr, SebastianUniBi ; Lamm, Tobias; Schmid, Tobias; Schnaubelt, Roland
Abstract / Bemerkung
We show the local wellposedness of biharmonic wave maps with initial data of sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of the gradient of the solutions. In contrast to the wave maps equation we use a vanishing viscosity argument and an appropriate parabolic regularization in order to obtain the existence result. The geometric nature of the equation is exploited to prove convergence of approximate solutions, uniqueness of the limit, and continuous dependence on initial data.
Erscheinungsjahr
2020
Zeitschriftentitel
Nonlinearity
Band
33
Ausgabe
5
Seite(n)
2270-2305
Page URI
https://pub.uni-bielefeld.de/record/2934334

Zitieren

Herr S, Lamm T, Schmid T, Schnaubelt R. Biharmonic wave maps: Local wellposedness in high regularity. Nonlinearity. 2020;33(5):2270-2305.
Herr, S., Lamm, T., Schmid, T., & Schnaubelt, R. (2020). Biharmonic wave maps: Local wellposedness in high regularity. Nonlinearity, 33(5), 2270-2305. doi:10.1088/1361-6544/ab73ce
Herr, S., Lamm, T., Schmid, T., and Schnaubelt, R. (2020). Biharmonic wave maps: Local wellposedness in high regularity. Nonlinearity 33, 2270-2305.
Herr, S., et al., 2020. Biharmonic wave maps: Local wellposedness in high regularity. Nonlinearity, 33(5), p 2270-2305.
S. Herr, et al., “Biharmonic wave maps: Local wellposedness in high regularity”, Nonlinearity, vol. 33, 2020, pp. 2270-2305.
Herr, S., Lamm, T., Schmid, T., Schnaubelt, R.: Biharmonic wave maps: Local wellposedness in high regularity. Nonlinearity. 33, 2270-2305 (2020).
Herr, Sebastian, Lamm, Tobias, Schmid, Tobias, and Schnaubelt, Roland. “Biharmonic wave maps: Local wellposedness in high regularity”. Nonlinearity 33.5 (2020): 2270-2305.
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