H "older Continuity of the Data to Solution Map for HR in the Weak\n Topology

2011/11/24 by David Karapetyan, Karapetyan, David
Computer Science · Mathematics · #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1111.5879

Abstract

It is shown that the data to solution map for the hyperelastic rod equation\nis H "older continuous from bounded sets of Sobolev spaces with exponent s >\n3/2 measured in a weaker Sobolev norm with index r < s in both the periodic\nand non-periodic cases. The proof is based on energy estimates coupled with a\ndelicate commutator estimate and multiplier estimate.\n

Citations

• Global Conservative Solutions of the Camassa–Holm Equation
• The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations

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