Journal
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
Volume 102, Issue 10, Pages -Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/zamm.202100567
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Funding
- National Natural Science Foundation of China [11871140, 12071065]
- National Key Research and Development Program of China [2020YFA0713602, 2020YFC1808301]
- Natural Science Foundation of Gansu Province [21JR7RA552]
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This paper investigates the global solutions for the modified Camassa-Holm equation. The global existence and uniqueness of strong solutions for the initial datum u(0)(x) belonging to H-s(R) with s>3/2 are obtained. Additionally, norm estimates for strong solutions and its momentum density are provided. Moreover, by utilizing the compensated compactness method and regularization technique, the global existence and uniqueness of weak solutions for the initial datum u(0)(x) belonging to H-1(R) are established.
This paper is concerned with the global solutions for the modified Camassa-Holm equation. We first obtain the global existence and uniqueness of strong solutions for the initial datum u(0)(x)is an element of H-s(R) with s>3/2, and then give some norm estimates of strong solutions and its momentum density. Finally, by using the compensated compactness method and regularization technique, we establish the global existence and uniqueness of weak solutions for the initial datum u(0)(x)is an element of H-1(R).
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