Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Torstein Nilssen"'
Publikováno v:
Stochastic Processes and their Applications. 130:2159-2184
We introduce a new technique for studying well posedness and energy estimates for evolution equations with a rough transport term. The technique is based on finding suitable space–time weight functions for the equations at hand. As an example we st
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::48a22edd4363555cc6d3118568dd861b
https://doi.org/10.1016/j.spa.2019.06.014
https://doi.org/10.1016/j.spa.2019.06.014
Publikováno v:
Journal of Differential Equations
Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For $\alpha\in (1/3,1/2)$, we give criteria for when we can approximate Banach space-valued weakly geometric $\alpha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb9bca81769f97afe5dcfc588739abd6
https://hdl.handle.net/11250/3022873
https://hdl.handle.net/11250/3022873
Publikováno v:
Journal of Functional Analysis
The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressible flow of an ideal fluid whose Lagrangian transport velocity possess
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d04c470513b7e90b5a77d56e501d1ca0
http://arxiv.org/abs/2104.14933
http://arxiv.org/abs/2104.14933
Publikováno v:
Advances in Mathematics
In this paper, we introduce a new framework for parametrization schemes (PS) in GFD. Using the theory of controlled rough paths, we derive a class of rough geophysical fluid dynamics (RGFD) models as critical points of rough action functionals. These
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bc85b27fb1331a46e3132e76b4956ac8
http://arxiv.org/abs/2004.07829
http://arxiv.org/abs/2004.07829
Autor:
Antoine Hocquet, Torstein Nilssen
Publikováno v:
Potential Analysis
We investigate existence, uniqueness and regularity for solutions of rough parabolic equations of the form $\partial _{t}u-A_{t}u-f=(\dot X_{t}(x) \cdot \nabla + \dot Y_{t}(x))u$ ∂ t u − A t u − f = ( X ̇ t ( x ) ⋅ ∇ + Y ̇ t ( x ) ) u on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f2f773023d7e4d8dfdf7d2b592b1ccc7
https://hdl.handle.net/11250/2992835
https://hdl.handle.net/11250/2992835
In this paper we present a new method for the construction of strong solutions of SDE’s with merely integrable drift coefficients driven by a multidimensional fractional Brownian motion with Hurst parameter $$H
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3f2562c6ec9e7a6666e30617801dfd28
http://hdl.handle.net/10852/75081
http://hdl.handle.net/10852/75081
Publikováno v:
Gerasimovičs, A, Hocquet, A & Nilssen, T 2021, ' Non-autonomous rough semilinear PDEs and the multiplicative Sewing lemma ', Journal of Functional Analysis, vol. 281, no. 10, 109200 . https://doi.org/10.1016/j.jfa.2021.109200
We investigate existence, uniqueness and regularity for local solutions of rough parabolic equations with subcritical noise of the form $du_t- L_tu_tdt= N(u_t)dt + \sum_{i = 1}^dF_i(u_t)d\mathbf X^i_t$ where $(L_t)_{t\in[0,T]}$ is a time-dependent fa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0196063f9ffff5441e8eb4bb7a9a549d
We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In pa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f399a28412479a98e60ed62e38e49769
Autor:
Torstein Nilssen
Publikováno v:
Stochastics. 88:779-802
In this paper we develop a method for constructing strong solutions of one-dimensional Stochastic Differential Equations where the drift may be discontinuous and unbounded. The driving noise is the Brownian Motion and we show that the solution is Sob
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4d3135e2e3a99ed3ec9be2ab04aed4e3
https://doi.org/10.1080/17442508.2016.1144755
https://doi.org/10.1080/17442508.2016.1144755
We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on R d using the variational approach. This includes well-posedness of (possibly degenerate) linear rough PDE's in L p ( R d ) , and then – based on a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05c4cc8811c3eed99de9ee01650b5ee5
http://arxiv.org/abs/1809.00841
http://arxiv.org/abs/1809.00841