A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects
| Autor: | Wen Yang, Aleks Jevnikar |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Inequality
Turbulence General Mathematics media_common.quotation_subject Mathematical analysis Mathematics::Analysis of PDEs 01 natural sciences 010305 fluids & plasmas Vortex Mathematics - Analysis of PDEs Argument Mean field equation Phenomenon 0103 physical sciences FOS: Mathematics 35J61 35J20 35R01 35B44 010306 general physics Analysis of PDEs (math.AP) Variable (mathematics) Mathematics Probability measure media_common |
| Zdroj: | Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 149:325-352 |
| ISSN: | 1473-7124 0308-2105 |
| Popis: | We are concerned with an elliptic problem which describes a mean field equation of the equilibrium turbulence of vortices with variable intensities. In the first part of the paper, we describe the blow-up picture and highlight the differences from the standard mean field equation as we observe non-quantization phenomenon. In the second part, we discuss the Moser–Trudinger inequality in terms of the blow-up masses and get the existence of solutions in a non-coercive regime by means of a variational argument, which is based on some improved Moser–Trudinger inequalities. |
| Databáze: | OpenAIRE |
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