Polynomial Bound and Nonlinear Smoothing for the Benjamin-Ono Equation on the Circle
| Autor: | Bradley Isom, Seungly Oh, Dionyssios Mantzavinos, Atanas Stefanov |
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| Rok vydání: | 2020 |
| Předmět: |
Polynomial
Pure mathematics Applied Mathematics 010102 general mathematics Mathematics::Analysis of PDEs Gauge (firearms) 01 natural sciences Free solution Benjamin–Ono equation 010101 applied mathematics Sobolev space Mathematics - Analysis of PDEs Nonlinear smoothing FOS: Mathematics Initial value problem 0101 mathematics Analysis Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2001.06896 |
| Popis: | For initial data in Sobolev spaces H s ( T ) , 1 2 s ⩽ 1 , the solution to the Cauchy problem for the Benjamin-Ono equation on the circle is shown to grow at most polynomially in time at a rate ( 1 + t ) 3 ( s − 1 2 ) + ϵ , 0 ϵ ≪ 1 . The key to establishing this result is the discovery of a nonlinear smoothing effect for the Benjamin-Ono equation, according to which the solution to the equation satisfied by a certain gauge transform, which is widely used in the well-posedness theory of the Cauchy problem, becomes smoother once its free solution is removed. |
| Databáze: | OpenAIRE |
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