F. Bouchut and L. Desvillettes, Averaging Lemmas without time Fourier transform and applications to discretized kinetic equations. Proc. Roy. Soc. Edinburgh, 129A (1999), 19--36. Home/Search Document Details and Download
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A Limiting Case for Velocity Averaging - Perthame, Souganidis (1998) (4 citations) (Correct)
....[BGPS] R. J. DiPerna and P. L. Lions [DL] Applications to hyperbolic equations are due to P. L. Lions, B. Perthame and E. Tadmor [LPT] Extensions of averaging compactness to discrete times have been used by L. Desvillettes and S. Mischler [DM] and generalized by F. Bouchut and L. Desvillettes [BD]. A limiting case of the averaging lemmas was obtained by P. G erard [G1] G2] who showed that if the sequence fgngn1 is compact in L 2 (IR 2d 1 ) then the corresponding averages supply a family ae n which is compact in L 2 (IR d 1 ) Here, we develop a new approach based on a ....
F. Bouchut and L. Desvillettes. Averaging lemmas without time Fourier transform and applications to discretized kinetic equations. Preprint.
Introduction to the Mathematical Theory of Kinetic Equations - Bouchut (1998) (1 citation) (Correct)
....account the relation h = Ff ) With a Gronwall lemma, we then get an estimate similar to (4. 7) see [12] for the details) 5 Averaging lemmas The so called averaging lemmas have been introduced in [15] and [14] and have been developed in the articles [7] 10] 13] 9] 4] 27] 24] 30] [3]. They express that if a function f(x; v) and a(v) Delta r x f(x; v) locally belong to some space, typically L p xv , then the average in velocity of f with respect to a smooth function (v) with compact support is more regular than f . In practice, this allows to obtain the local compactness of ....
....a(v) Delta ) i( a(v) Delta ) i( a(v) Delta ) 5.64) which gives by taking F Gamma1 t ffi(t) 1I t 0 e Gammat( ia(v) Delta ) 1I t 0 e Gammat( ia(v) Delta ) t [ t ia(v) Delta )ffi(t) 5. 65) This decomposition is used by Bouchut and Desvillettes [3]. It has support in t 0, and thus is adapted to the Cauchy problem. In the case of a full derivative in L p , we have the following result from [30] Theorem 5.9 Under the same assumptions as in Theorem 5.6 with fi = 1 and if div x a(v)f = div x X jffjm ff v g ff ; 5.66) we have fl ....
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F. Bouchut, L. Desvillettes, Averaging lemmas without time Fourier transform and applications to discretized kinetic equations, Proc. Royal Soc. Edinburgh, 129A, (1999), 19--36.
Relaxation to isentropic gas dynamics for a BGK system with .. - Berthelin, Bouchut Self-citation (Bouchut) (Correct)
....0 dtdxd H F ; 2.50) which gives the bound on the rst component. Furthermore, 1I M [f ] 0 (f ) A 1I M [f ] 0 (f ) A ; 2.51) which concludes the proof. 3 Averaging The regularity theory for averages of kinetic equations has been developed in [14] 13] [9], 22] 10] 18] 8] We introduce here a result that is particularly adapted to BGK right hand sides. In order to treat correctly the initial data, we use a Fourier transform in the variable x only, in the spirit of [9] The dual variable is denoted by k. Proposition 3.1 Let a 2 L loc ....
....theory for averages of kinetic equations has been developed in [14] 13] 9] 22] 10] 18] 8] We introduce here a result that is particularly adapted to BGK right hand sides. In order to treat correctly the initial data, we use a Fourier transform in the variable x only, in the spirit of [9]. The dual variable is denoted by k. Proposition 3.1 Let a 2 L loc (R ; R ) and 2 L ) such that for some K 0 and 0 1, one has 8 2 S N 1 ; 8 z 2 R; 8 0; z a( z j ( j d K : 3.1) Let f 2 C( 0; T ] L ) solve t f div x [a( f ] ....
[Article contains additional citation context not shown here]
F. Bouchut, L. Desvillettes, Averaging lemmas without time Fourier transform and application to discretized kinetic equations, Proceedings of the Royal Society of Edinburgh 129A (1999), 19-36.
Relaxation to Isentropic Gas Dynamics for a BGK System with .. - Berthelin, Bouchut (2003) Self-citation (Bouchut) (Correct)
....0 dtdxd H F ; 2.50) which gives the bound on the first component. Furthermore, 1I M [f ] 0 (f ) A 1I M [f ] 0 (f ) A ; 2.51) which concludes the proof. 3 Averaging The regularity theory for averages of kinetic equations has been developed in [14] 13] [9], 22] 10] 18] 8] We introduce here a result that is particularly adapted to BGK right hand sides. In order to treat correctly the initial data, we use a Fourier transform in the variable x only, in the spirit of [9] The dual variable is denoted by k. Proposition 3.1 Let a 2 L loc ....
....theory for averages of kinetic equations has been developed in [14] 13] 9] 22] 10] 18] 8] We introduce here a result that is particularly adapted to BGK right hand sides. In order to treat correctly the initial data, we use a Fourier transform in the variable x only, in the spirit of [9]. The dual variable is denoted by k. Proposition 3.1 Let a 2 L loc (R ; R ) and 2 L ) such that for some K 0 and 0 ff 1, one has 8 oe 2 S N Gamma1 ; 8 z 2 R; 8 j 0; z a( Deltaoe z j j ( j d Kj : 3.1) Let f 2 C( 0; T ] L ) solve t f div x [a( f ....
[Article contains additional citation context not shown here]
F. Bouchut, L. Desvillettes, Averaging lemmas without time Fourier transform and application to discretized kinetic equations, Proceedings of the Royal Society of Edinburgh 129A (1999), 19-36.
Hypoelliptic Regularity in Kinetic Equations - Bouchut (2003) (2 citations) Self-citation (Bouchut) (Correct)
.... Subject Classification: 35H10, 82C40, 35B65 Contents 1 Introduction and main results 2 2 The Fourier method 5 3 The Hormander commutator 18 4 The characteristics commutator 20 1 Introduction and main results The classical averaging theory, developed in [11] 10] 9] 1] 14] [3], 15] 4] 5] state that the solution f(t; x; v) to a kinetic equation, say t f v Delta r x f = g in R t Theta R v ; 1.1) has some regularity when averaged with respect to the velocity v. More precisely, if f , g 2 L v ) then the average ae (t; x) f(t; x; v) v) dv ....
F. Bouchut, L. Desvillettes, Averaging lemmas without time Fourier transform and application to discretized kinetic equations, Proc. of the Royal Soc. of Edinburgh 129A (1999), 19-36.
On The Singularities Of The Global Small Solutions Of The.. - Boudin, DESVILLETTES (2000) (1 citation) Self-citation (Desvillettes) (Correct)
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F. Bouchut, L. Desvillettes. Averaging lemmas without time Fourier transform and application to discretized kinetic equations. Proc. Roy. Soc. Ed., 129A : 19--36, 1999.
A Real Space Method for Averaging Lemmas - Jabin, Vega (2003) (Correct)
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F. Bouchut and L. Desvillettes, Averaging Lemmas without time Fourier transform and applications to discretized kinetic equations. Proc. Roy. Soc. Edinburgh, 129A (1999), 19--36.
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